CATALOGUE MATHEMATICAL TABLES

Those are the dinosaurs of mathematical calculation.

Up to quite recently all calculations were made using pencil, paper and the human brain. However all more complex calculations than adding and substracting are quite time-consuming. Thus a table of logarithms enabling the reduction of a multiplication to an addition and of a division to a substraction is quite a powerfull tool in reducing the time spent in calculation. The man years invested in their preparation seemed a sound investment.

The use of those tables was therefore taught to me in secondary school around 1960. However in courses on statistics thereafter in university it was pointed out, that such calculation was too inexact . As a result of a 3 hours exam 2½ were spent on manual calculation.

Nevertheless extensive use was made of tables of logarithms in astronomy, geometry, compound interest calculation and related actuarial applications.

The calculators dream of a machine calculated table printed automatically [thus eliminating printing errors was finally realised in the 1972 Tilburg interest table [book 13101]. However the Japanese pocket calculators becoming available a few years later and the PC in the beginning of the ‘80’s made even this perfect table completely without use. Quite a dramatic development in less then 10 years.

Prices

Those titles are not for sale, and only are a documentation of copies presently in THE STOA COLLECTION. However the late Max Israel once told me, that descriptions without prices were a bit of less interest to him. For that reason my best estimates of a possible price in the retail sales-catalogue of a high-end antiquarian bookseller are stated.

Some titles were sold in the past or in other collections as indicated, and are included here for reason of their general interest.

NAPIERIAN LOGARITHMS

[033629] Napier, John. Logarithmorum canonis descriptio, sev arithmeticarum supputationum mirabilis abbreviatio. Eiusque usus in utraque trigonometria, ut etiam in omni logistica mathematica ... explicatio. [and [2^nd title] Mirifici logarithmorum canonis constructio; et eorum ad Natvrales ipsorum numeros habitudines]. Lyon: Barthold Vincent, 1619. The Constructio with a separate titlepage dated 1620. Second (and first continental) edition. Ursinus, who completed a more extensive table in 1624 [see the following book 23462], quotes this edition in the introduction thereof.

COLLATION

(8), 56, (92) and 62, (2) pp. 4to, A to H in fours, A to L in fours M in two and A to H in fours. Titles in red and black. Leave D3 of the 1st sequence wrongly marked D5. Extraict du Privilege du Roy dated 1 October 1619 on verso of M2 and another one on the last H4 recto dated 31 March 1620. Identical to the most complete copies McDonald collated. In the BNF copy verso M2 is blank however. In a copy recently offered by Heritage the last H4 is blank.

CONDITION

Contemporary limp vellum, stained and worn, preserved in a modern cloth box. Some browning throughout, some browning and dampstaining to the first and last leaves. Cancelled ownership inscriptions to title. Slight worming to gutter of a few leaves.

REFERENCES

MacDonald p. 141-144, Honeyman 2292 (with a 1620 Descriptio however), Henderson 6.0., Fletcher p. 419. Tomash N5 [with 1620 Descriptio]. Quite a lot of copies in COPAC, NCC (Leiden and Groningen) and KvK, however most copies with both titles dated 1620 . The only other copy with 1619 on the title of the Descriptio is at BNF, Paris. Also MacDonald could not locate another such copy in 1889 (see below for a further explanation). In 1915 however an other copy was shown at the Napier Tercentenary (#11), belonging to Archibald Scott Napier. That copy seems to miss the Extraict in the end on H4 (see also 12, were this is described as addition). Ursinus refers to the 1620 Lyon edition (see p. 178 of his 1624 tables).

PROVENANCE

A. R. Michaelis [1916-2001], his bookplate at fpep. He was scientific journalist mostly publishing in the UK Daily Telegraph. His book publications vary from FROM SEMAPHORE TO SATELITE (100 YEARS OF TELECOMMUNICATION), 1965 to SCIENTIFIC TEMPER, 2001. In the last book (p. 97) he tells us: When my collecting of old scientific instruments became too expensive, I changed my acquisitive activities to books, for which London of course was an ideal place. Even if I could not afford a first edition.... I was happy to spend GBP 100 for Napier's first Continental edition, Lugduvini 1619, of his Logarithmorum Canonis. It is the first Table of Logarithms ever published on he Europeaan Continent, in the same year as the Editio Princeps appeared in Scotland. In the same book Michaelis tells us, that the larger part of his collection went to Hochschule Holzen when he moved from London to Heidelberg in 1996. Evidently he retained this Napier, which came into the market after his death.

CONTENTS

A copy of the very first table of Napierian logarithms existing. This Lyon edition is a fairly correct reprint of the Edinburgh first editions of the Descriptio (1614) and Constructio (1619) as published by Andreas Hart In those log e (2.302585...) is 1 and not log 10 as in decimal logs used universely since 1628 (the first Vlacq tables). Napier's table (1614) is to minutes in 7 decimals, in 1624 extended by Ursinus to 10'' in 8 decimals, also giving 1st differences. The tables have the following main columns: natural sines, log sines, log tangens, log cosines and cosines. Napier marks the logtan column differentiae, as sin/cos=tan. Consequently logtan can be found by deducting logcos from logsin. As sin x=cos(90-x) the table runs to 44.60' , higher values for sin being found in the corresponding cosin column and vice versa. For easy reference those higher values are indicated at the bottom of the page, an arrangement introduced by Rheticus in 1551 and usual ever since. Napier's table essentially consists of interpolations of the "Radical Table " developed by him (see Constructio p. 47). In this table the sines develop geometrically with a factor 9995/10000 and the corresponding logarithms develop arithmetically by the equal interval 5001.25. However in this progression a calculating error was made, resulting in logsin 30 ending 69, were Ursinus gives 718, a difference of 28 (note that Ursinus gives 1 more decimal than Napier). My pocket Casio calculator agrees with Ursinus. This error in Napier was first noted by Edward Sang in 1865, Ursinus does not refer to it. Concerning the dating 1619 of the Constructio MacDonald remarks: On the issue of the Edinburgh edition of 1619, Barthold Vincent would appear to have set out at once about the preparation of an edition for issue at Lyon with the date 1619 on title. ......A possible explanation of this may be that the title-page was originally set up with the date M DC IX,but when it was found that the whole work could not be issued in that year, the date was altered to M DC XX, and a few copies may have been printed before the alteration. The only copy we have found is in the Bibliotheque Nationale. € 11.000,00

[023462] Ursinus, Benjamin. TRIGONOMETRIA CUM MAGNO LOGARITHMOR. CANONE. Colonia: Georg Runge for Martin Gutt, 1625. First Edition.

COLLATION

4to [193*155 mm]. The 2nd part (the Canon) with a seperate titlepage: Benjamin Ursinus, MAGNUS CANON TRIANGULORUM LOGARITHMICUS, Colonia, Georg Runge for Martin Gutt, 1624. (4), 272, (454) pp. The 1st. unnumbered page is the engraved title marked: Petrus Rollos fecit, the title being on a swinging door in perspective, also described by Henderson, most likely using the Oxford copy. Also the typo he describes (Guttij tipys) can be found on this page. The swinging

door is earlier seen on Salomon de Caus, Les raisons des forces mouvantes, Frankfurt, Norton, 1615 (offered by Interlibrum 253/36). The last leave has errata and a colophon dated 1624 on the verso. The 2nd title with blank verso, thus 225 leaves remaining for the tables (5 leaves per degree). All quires in 4, last in 3. Leave 2 and 3 are 1 sheet however, folded at spine. Most descriptions give 227 leaves for the Canon, Macdonald (p. 158) however mentions a blank leave Lll4, which he possibly noted in one of the UK copies. Signatures:):(4 A-Z4 Aa-LL A-Z Aa-Zz Aaa-LLL

CONDITION

Contemporary overlapping orange (rare in that colour) vellum (in quite good condition, taking into account the age). In the past ages the vellum was protected from the hands of computers by plain paper wrappers, pasted under the endpapers. Those are now expertly removed. The wrappers are still available in a seperate envelope, and could easily be reinstalled to a future owners taste. Edges stained green. Some wear at corners and spine. Pages mildly browned, as often on books from the 30 Year War period (1618-1648). Contemporary handwritten expert notes , partly in red. The handwriting of those notes is quite like that of Bode's name on title.

PROVENANCE

1. On the lower pastedown endpaper are the names of 6 monks of the Ordine Trinitat Andrea, dated 1678.

2. Johann Justus Bode, 1719 and "Albrecht", neatly inscibed in the margin of the title, small stamp on dedication page. JJ Bode (1676-1719) was born in Bodenburg. He developed a sundial for travelers.

3. V. Zach [see illustration] The astronomer Franz Xaver von Zach (born Pest 1754) built and supervised the Seefeld observatory for Herzog Ernst II von Sachsen-Gotha-Altenburg in 1788. In the time it was the most modern observatory in Europe. See his Tabulae Motuum Solis [book 84280 in the Astronomy section] for further biographical facts on this important scientist.

Other books from this provenance are Napier (1614) and Kepler (1619) in the Milestones of Science Collection, Sparrow 149 and 115 and the Jena2 copy of Copernicus, De Revolutionibus (1543), see Gingerich, Census 2002 p. 73. The last copy is a Christmas 1793 gift of Ernst II to Von Zach, see inscription 2 in the Gingerich description.

CONTENTS

A copy of the most extensive table of Napierian logarithms existing. In those log e (2.302585...) is 1 and not log 10 as in decimal logs used universely since 1628 (the first Vlacq tables). Napier's table (1614) was to minutes in 7 decimals, extended by Ursinus to 10'' in 8 decimals, also giving 1st differences. The tables have the following main columns: natural sines, log sines, log tangens, log cosines and cosines, each with a D(ifference) column behind it. As sin x=cos(90-x) the table runs to 44.59' 50", higher values for sin being found in the corresponding cosin column and vice versa. For easy reference those higher values are indicated at the bottom of the page, as usual ever since. For some arcs often used even more exact values are calculated (16 decimals, see p. 139 ff. in the text).

Napier's table essentially consists of interpolations of the "Radical Table " developed by him (see Constructio 47). In this table the sines develop geometrically with a factor 9995/10000 and the corresponding logarithms develop arithmetically by the equal interval 5001.25. However in this progression a calculating error was made, resulting in logsin 30 ending 69, were Ursinus gives 718, a difference of 28 (note that Ursinus gives 1 more decimal than Napier). My pocket Casio calculator agrees with Ursinus. This error in Napier was first noted by Edward Sang in 1865, Ursinus does not refer to it. It can be concluded, that the Ursinus table is based on new calculations, and not just on interpolation of the Napier table.

OTHER MATTERS

Colonia is Kolln a d Spree nowedays part of Berlin. The different dating of Trigonometria and Canon suggest a Sammelband of 2 seperate issues, also the quires are lettered seperately. KvK mentions 1 separate table (Dusseldorf) and 3 books as described here (Cologne, Munster and Regensburg), actual copies possibly being not all as complete as our copy. COPAC has 3 complete copies (Oxford, BL and UCL), the collation of Oxford exactly agrees with ours. NCC has 1 complete copy (Groningen), with (autopsy 2/12/03) agrees with our collation plus the leave Lll4 found by Macdonald in some UK copies. In conclusion, the works are most likely issued together, an individual copy occurring occasionally, as with the Vlacq tables. Henderson 8.0, Fletcher p. 439 and 179, Dodson III, Macdonald 157 (including a very detailed collation, in agreement with the present copy except for a last blank leave Lll4). Tomash U6. Macdonald (1889) also mentions copies in Edinburgh and BNF, which cannot be traced nowadays (2012). Not in Honeyman (never found a copy?) Quite rare and not often seen in trade. OCLC adds 3 copies in the US (US Naval Obs., Clark and Un. Michigan). Leave Lll4 not in standard OCLC description, in which also collation of signatures (identical to our copy).

EVALUATION

Fletcher remarks on those tables (p. 179):It may be noticed that the 8-decimal Napierian canon of Ursinus 1624 has never been equalled subsequently. Further Eisenschmid (the editor of the 1700 edition of Kepler's Tabulae Manuales, see our book 33615, and thus a much more contemporary expert than the present bibliographer) states, that Bartsch (Keplers son in law and collaborator) used the Ursinus table, omitting the last 3 figures. Indeed the Tabulae Manuales are in 5 decimals. As those Tabulae Manuales are an extract of logarithms from the Tabulae Rudolphinae (1627, which use those logs for astronomical calculations), those famous Kepler tables are thus (according to Eisenschmid) based on Ursinus' logarithms! In this connection it also should be mentioned, that the cos-table in Kepler (1627) has an 10" interval, which only can come from Ursinus, Napier having a 60" (=minute) interval. Further Ursinus owned a copy of the 1627 Kepler tables (the Honeyman #1800 copy. Owen Gingerich states that it was acquired by the Adler Planetarium in Chicago) warmly inscribed to him, Kepler calling him and Tycho Brahe the scientific fathers of those tables (my free translation of the Latin text). As Brahe (died 1601) contributed much to the underlying astronomical observations, for Ursinus this remark must refer to his log tables. Those observations support the statement of Eisenschmid concerning the Ursinus source of the Kepler tables. € 7.200,00

Subtitle of part II

[033615] Kepler, Johannes and Jakob Bartsch. TABULAE MANUALES LOGARITHMICAE. Strassbourg: Theodor Ierse, 1700. 40, (276) pp. a4-e4, A4-LL4, MM2. 160*95 mm., however bound in fours. Introduction and 5 tables after seperate subtitles. 19th century marbled boards with handwritten title on label on spine. 1cm of blank missing at foot of title. The quite elaborate subtitle is: ad calculum astronomicum, in specie Tabb. Rudolphinarum compendiose tractandum mire utiles. Ob defectum prioris editionis Saganensis multum hactenus desideratae. Quibus accessit in hac editione introductio nova curante Joh. Casp. Eisenschmid.

Kepler's Tabulae Rudolphinarum (folio, Ulm, 1627) were astronomic tables, in which the tables of logarithms used for its calculation were also published. The present tables are in a more practical format (manuales), extracted from them in 1631 by Bartsch (Keplers son in law). However the edition (Sagan, 1631) misfired, Bartsch dying short after its publication, and only 2 incomplete copies (Koenigsberg and Bonn) are known (see also Caspar 85). In 1700 Eisenschmid (a Strassbourg professor, died in 1716) republished the Bartsch edited tables and added a new 9-page Praefatio. An important copy of the first generation of logarithms (as we would say in present day based on the natural number e) dominated by Napier in the UK and Kepler and Ursinus on the continent. The last 2 also worked together (see Honeyman 1800, Ursinus copy of the Tabulae of 1627). In 1628 the first complete version of Briggsian logarithms (based on 10) was published by Vlacq, and those were used until electronic calculators made logarithms obsolete around 1978.

Second and only procurable edition. Comparing the tables involved shows interesting results. Napier (1614) is 1 table showing log sin and log cosin with log tgn as differential of the first 2 in between at a 1' interval. The range is from 0-45 degrees. 7 decimals are shown. Ursinus (1624) has the same format and range with a 10" interval however, showing 8 decimals. In Kepler (1627) the data are shown in 3 seperate tables. Log sin at the same range and interval as Napier, decimals being reduced however from 7 to 5. The same goes for log tgn, however the range ends at 10 degrees. Log cosin is surprising: a 10" interval at the 0-1 degree 40' range. Kepler rounding to 5 decimals, the source of the first 2 tables cannot be determined, as the characteristic differences between Napier and Ursinus show only in higher decimals. The interval of the third table only can come from Ursinus. The interval and range of the present 1700 tables is increased considerably, largely to the Ursinus level. However the third table has a 2" interval, that Bartsch must have interpolated himself (Ursinus having a 10" interval). This 2" constitutes the smallest interval of any Napierian table known. Also Ursinus assisted Kepler from 1610 to 1614, and the Honeyman #1800 copy (a Kepler 1627 table warmly dedicated to Ursinus) shows they were still in contact that year. Therefore Kepler must have had a copy of Ursinus (1624) well before the publishing of his 1627 tables. In the above dedication further Kepler mentions Tycho Brahe and Ursinus as the scientific fathers of his 1627 tables. This altogether proves that the third table in Kepler (1627) can only come from Ursinus, and that Kepler himself was of the opinion, that Ursinus considerably contributed to it.

Henderson 12.1, not in Fletcher. Tomash K28. 4 copies in COPAC, 2 in NCC (Leiden and Utrecht). Weil 27/124. € 10.500,00

Kepler and logarithmic calculation

Keplers contribution to this subject is complex, as he was plagued by quite hectic circumstances, being between 1618 (when he became aware of Napiers invention) and his death in 1630:

-The witchcraft charge against his mother around 1620

-The 30 year war started in 1618

-The development of the subject by other authors (Ursinus, Briggs, Vlacq) in quick succession in a time with slow international communication.

Kepler was under pressure to complete the Rudolphine Tables, among others by his maecenas Rudolph II and the Brahe heirs. As a result he was forced into decisions, that later had to be revised in view of material newly published by other authors.

It must be said, that Kepler always has been quite open-minded in those revisions, however to understand both decisions and revisions a detailed analysis is clarifying.

Chilias 1624

In this table the value of sin(α) varies from 0 to 1 as α progresses from 0º to 90º. The table, newly calculated by Kepler, has those sin values as argument with a .001 interval. The logarithms given are positive however. As log1=0 thus in fact the logarithms of 1/ sin(α) are given (see also Fletcher 1945, p.179).

As Kepler mentions in a letter to Mästlin those new calculations state a value for log sin 30º of 69314.72, where Napier has 69 as the last 2 digits. The same error was rediscovered by Sang in 1865 when comparing the Napier table with that of Ursinus (which is also newly calculated).

Kepler evidently was quite proud of this novelty.

The frontispiece of the Tabula Rudolphinae shows on the roof 6 women impersonating the sciences, of which Arithmetica has a stick in her left hand and another one in her right hand of half lengh of the first, being the sides of a triangle relevant for the calculation of sin 30º=0.5.The correct value of log sin 30º is shown around her head. This curious detail does not fully apply to those tables however, as the logarithms included are in 5 digits and the difference thus does not show anymore.

Another novelty relates the proportions of 1 expressed in the argument column to the corresponding value in hours, minutes and seconds/24 hours (column 3) and in minutes and seconds/ degree (column 5). Those logistic values are of particular use in astronomical calculations, and the further development of this novelty in the TR must have been a major cause for the use of Keplers tables for astronomical applications until the end of the 18^th century.

Tabulae Rudolphinae 1627

The major part of those tables is of astronomical nature, describing the motion of the sun, moon and planets, the latitude and longitude of major cities and other basic astronomical data.

The beginning 23 pages also give logarithmic values to ease the astronomical calculations using the astronomical data on the later pages.

It is important to be aware, that the TR are a kind of root-tables, enabling the calculation of annual Ephemerides, being the positions of the sun, moon and planets in terms of actual date, time and location. The statement sometimes found, that those logarithms have been used calculating the TR therefore is at least incomplete, and possibly not correct.

The largest part of the logarithm section is taken by the first table titled Heptacosias Logarithmorum Logisticorum, elaborating the concept introduced in the Chilias of directly supplying logarithms of logistic values. Those are newly computed, opting for intervals more appropriate for logistic values than the .001 interval of the Chilias.

In a separate table the logarithms of sin(α) are given at a 1’ interval (0º<α<90º) at 2 decimals less than in Napiers table. As a result Kepler could prepare this table from that of Napier, as the error discussed in the preceeding paragraph vanishes in the rounding.

Some minor specifics of the last decimals show, that Kepler actually used values rounded from Napier in this table, as is illustrated by the following values of log sin:

	3º 45'	14º 10'
Ursinus	272718517	140754520
Napier	27271843	14075447
Kepler	272718	140754

Separate tables are given for the logarithms of cos and tan at ranges and intervals appropriate for use in astronomy calculations.

Appendix Bartschii 1629

Bartsch completed his appendix in 1629, and it is not present in most copies of the TR. The following quotes come from the more complete GW. Bartsch is more practical in advising his users on supplementary material being available in the meantime as follows:

Si vero laborem… cupit, substituere potest Ursinus (1624), uso magno, exactissime ad dena secunda descriptum, aut meos manuales, ex eodem cum ipsius venia derivatos, qui paucioribus pagellis compendiose descripti,…(If it is required to work more exactly, it can be replaced by Ursinus (1624), which is extremely useful and at a 10 second interval, or by my Tabulae Manuales , which are extracted from the work mentioned last with permission, and which in less pages describe the matter in a more condensed way,..) GW X 267.

Hammer states in his Nachbericht to Keplers Gesammelte Werke (X p.51*): Without any doubt Kepler would have been of great service to his users, in case he had decided to use logarithms of the Briggsian type in the TR. The issue of the Kepler Heptacosias fivefold enlarged by Jacob Bartsch in 1700 than would not have been necessary.

Bartsch and Hammer touch on three items here, of which the significance possibly becomes more clear, when they are dealt with seperately:

Briggs 1628

Possibly Hammer is right, however in practice this option has never been open to Kepler. Hammer himself states (GW X 21*) that the manuscript of the TR was largely finished in middle 1624. Briggsian logarithms of trigoniometrical functions only became available in 1628.

Ursinus 1624

Benjamin Ursinus assisted Kepler before 1620. His Magnus Canon became available in early 1625 (the dating of the intro paragraphs), and states the logarithms of trigoniometrical values at 3 decimals more (see above) than the TR and at a 10” internal (TR 1’). This is too late to be taken into account in the text of the TR, completed in manuscipt in mid 1624. The Bartsch Appendix is from 1629 however and thus can mention it as very well supplementing the more concise logaritmic section in the TR.

Also Kepler has shown to be quite welcoming to the Magnus Canon. Ursinus owned a copy of the 1627 Kepler tables (the Honeyman #1800 copy. Owen Gingerich states that it was acquired by the Adler Planetarium in Chicago) warmly inscribed to him, Kepler calling him and Tycho Brahe "the scientific fathers of those tables" (my free translation of the Latin text). As Brahe (died 1601) contributed much to the underlying astronomical observations, for Ursinus this remark must refer to his log tables.

The provenance of our copy of Ursinus (1624) includes the major astronomer Franz von Zach, whose activities culminated around 1800. 175 years after publication his interest in the book can only be understood in connection with the TR.

Bartsch and Kepler could recommend the use of Ursinus (1624) because it avoids the error in the last 2 decimals of the Napier table, and even adds one other decimal.

Bartsch, Tabulae Manuales 1700

The significance of this title is twofold.

It summarizes Ursinus (1624) omitting the last 3 decimals, however maintaining the 10” interval, it enlarges that of the TR.

On the other hand it enlarges the Heptacosias table fivefold, the area being of special importance for astronomical calculations, because of the direct link of logistic values to its logarithms.

Maybe this is the major explanation of the continued use of the triad TR/Magnus Canon/ Tabulae Manuales for 175 years, combining the astronomical data of the TR with the most complete trigoniometrical logarithms of the Magna Canon and the smaller interval of the Heptacosias in the Manuales.

Indeed Bartsch did complete the Tabulae Manuales at the time of his writing the 1629 Appendix to TR, however the edition (Sagan, 1631) misfired, Bartsch dying short after its publication, and only 2 incomplete copies (Koenigsberg and Bonn) are known (see also Caspar 85) to survive.

In 1700 Eisenschmid (a Strassbourg mathematics professor, † 1716) corrected and republished the Bartsch tables and added a new 9-page Praefatio. Such a reissue after 69 years can only be understood as an appreciation by contemporary astronomers of the extension of the Heptacosias given.

Evaluation

Purely from a calculus point of view the Heptacosias in the Manuales and the logarithmic values of trigoniometrical functions in the Magnus Canon are necessary additions to the TR in their use for astronomical calculations, as is illustrated by their recommendation by Kepler and Bartsch, the reissue of the Manuales as late as 1700 and the presence of the Canon in the library of Von Zach (*1754). This makes the TR themselves less interesting within a calculus-oriented collecting scope.

For Manuales see 33615 and for the Ursinus’ Magnus Canon 23462.

BRIGGSIAN LOGARITHMS

[053959] Briggs, Henry. ARITHMETICA LOGARITHMICA sive Logarithmorum Chiliades triginta pro numeris naturali serie crescentibus ab unitate ad 2oooo et a 90ooo ad 1ooooo, ... hos numeros primus invenit . William Jones, 1624. First Edition. (8), 88, 300 pp. Collation A4 b-m4 A-Q6 R4 Hhhh8 Iiii6-Oooo6 *6. Page 15 incorrectly numbered 17. Folio (325*205 mm.). Contemporary calf, quadruple blind-tooled fillet borders (rebacked); in cloth drop-back box. fpep with contemporary latin printed text. FIRST EDITION of Briggs' tables of logarithms which formed the basis of printed mathematical tables for many years.

Briggs received his M.A. from Cambridge University in 1585, and served as an examiner and lecturer in mathematics there before becoming the first professor of geometry at London's newly founded Gresham College. He spent many years working on problems of navigation and astronomy, but by 1615 had turned his attention entirely to logarithms, which he learned of through the publication of Napier's Mirifici logarithmorum canonis descriptio (1614). While visiting Napier in Scotland during the summers of 1615 and 1616, Briggs discussed with Napier the prospect of changing the latter's original hyperbolic system. Napier's failing health prevented him from undertaking this task, so the job fell to Briggs, who in 1617 published his Logarithmorum chilias prima, containing the first 1000 logarithms of the new canon.

This was followed seven years later by his Arithmetica logarithmica, which contained logarithms from 1 to 20,000 and from 90,000 to 100,000; the remaining 70 chiliads, supplied by Adrian Vlacq, were published in the second edition of 1628.

Provenance: Signature C. Mason on title (? Charles Mason, astronomer, 1730--87 ?). E. N. da C. Andrade (1887-1971) and Haskell F. Norman (1915-96), see their bookplates at ffep. March 1928 this copy (in Andrade's hand), cutout from a Blackwell catalog item 463 tipped in at fpep. Sold by the order of the governing body, stamp at ffep with illegable signature and date 1908. Henderson 18.0. Fletcher p. 111. Tomash B250. Hook and Norman 1991, no. 339. OOC 2 [this copy]. € 9.500,00

[023227] Decker, Ezechiel De. TWEEDE DEEL VAN DE NIEVWE TEL-KONST 1627. Gouda: Pieter Rammaseyn, 1627. 23, (9), 36, (8) pp. 190*260 mm. Original white boards with black title on spine. In original glassine, with restauration at top of spine. 1 of 500 facsimile copies of the only copy extant, that was discovered in the library of the insurance company Utrecht in 1926. Nieuwkoop, B. de Graaf , 1964. Introduction by A. J. E. M. Smeur (the 23 p.), title Telkonst, Druck-fauten, voorrede by Den Decker and 7 chapters explanations, all in Dutch. Of the tables p1 (numbers 1-150) and a later page (numbers 19951-20100) are included.

Those pages are identical to the pages found in my copy of Briggs/Vlacq, ARITHMETIQUE LOGARITHMETIQUE (1628, same publisher), only the size being smaller in the facsimile (due to reduction upon reproduction. A printing error of log 80 is in both copies. Also the page stating errata are identical in both copies. In his intro Den Decker announces editions in Latin and French (as indeed were published in 1628) and German (which did not materialize) edited by Vlacq. Goniometrical tables are only in the 1628 editions. Thus the TEL-KONST is in fact a prepublication in Dutch of the material ready in 1627. € 100,00

[023165] Briggs, Henry, traduit (Description), augmentee (Premiere table) et composee (Deuxieme Table) par Adriaen Vlacq. ARITHMETIQUE LOGARITHMETIQUE OU LA CONSTRUCTION ET USAGE D'UNE TABLE CONTENANT Les Logarihmes Detous Les Nombres Depuis l'Unite Jusques a 100000. Et D'UNE AUTRE TABLE EN laquelle sont Comprins les Logarithmes des Sinus, Tangentes & Secantes.... . Gouda: Pierre Rammasein, 1628. First Edition. (8), 84, (672), (92) pp. Signatures: ***4, a-g6, A-Z6, Aa-Zz6, Aaa-Rrr6, Sss4 (last verso blank) 325*210 mm. Later (1809?, see provenance) marbled boards with gilt title (LOGARITHMEN VON VLACQ) in red letterpiece on spine. Title in black and red. Edgewear all around, however a still very solid copy. Good hinges. Minor browning, 3 small holes in title. PROVENANCE: G. Wagner, 1809, his small and neat name on ffep and two earlier names on title.

Contains log 1-100.000 and logsin logtan logsecans per minute both in 10 decimals. The second part with a Latin subtitle. Henderson also discusses a subtitle of part 1, which he has seen in Latin and Dutch. It is not in our copy (instead a blank unmarked A1 leave). Possibly only in the Latin edition. After invention of the logarithms by Napier (also referred to in the title of this work) in 1611 the first table ever calculated was published by Briggs in 1624. This included however only the numbers 1-20.000 and 90.000-100.000. For this edition Vlacq used those tables and completed (computing 10 decimals) it with the logarithms 20.001-89.999 (thus in first publication ever), which constitutes the "premiere partie". As this interval has 6415 primes, this mainly involved recalculation by addition. Additional to the errata the numbers 4776-4780 are misstated as 3376-3380, an old errata slip glued over. He further prepared the goniometric tables in the "seconde partie", also not preceeded by any other version. Lastly Briggs prepared the Descriptio, all described items being published in 1628, constituting the latin edition. Vlacq further almost completely translated Briggs Descriptio in French. The present edition includes that translation and further the tables being from the same type in the Latin and French edition. As such it constitutes the first vulgar publication of the Descriptio and the first complete table of logarithms ever published. The intro leaves include a sheet of errata. Henderson 24.1, Fletcher p. 440, Sampson 30, Honeyman 505. Huygens folio 32. 5 copies in COPAC, of which one (Leeds) with a collated description, having 7 intro pages (possibly not counting p. 8, which is blank). Further identical to our collation. 4 copies in NCC, none collated. According to Bierens de Haan Vlacq's work was published simultaneously in French, Dutch, Latin and English (London 1631, printed by George Miller, see Sampson 33), with a total of 1000 copies (also mentioned by Briggs to Pell, see Smeur (1964) p.13, our book 23227). Also the facsimile of Den Decker's TWEEDE DEEL DER NIEUWE TELKONST therein has type identical to the premiere partie of our copy. The first complete logarithm tables ever published, however with less detail than the Briggs tables, which are accurate to 14 decimals. Acquired from old stock of B M Israel after Max's death in 2001. Henderson 24.1, Fletcher p. 111 and 440. Tomash V22. € 4.000,00

[033791] Briggs, Henry; (Vlacq, Adriaan). LOGARITHMICALL ARITHMETIKE. London: George Miller, 1631. (2), 54, (764), (8), (2) pp. , being title and blank verso, English introduction, table of logarithms of numbers (titled: Tafel der Logarithmi voor de Ghetallen van 1 af tot 100000), table of trigonometrical logarithms (with the usual Latin title CANON TRIANGULORUM...etc), table of lattitudes and Faulds escaped amend thus. Signatures A-G4, A-Rrr6, Sss4, H4, none1, the last leave being quite rare errata [see below].

The tables (except those of lattitudes) are from sheets printed by Rammensein (Gouda, The Netherlands) in 1627. The subtitles are identical to those on the tables in TWEEDE DEEL DER NIEUWE TELKONST by Ezechiel den Decker. Den Decker and Vlacq cooperated on the table project ( see 23165 a copy of the French 1728 edition for further details). The only existing copy of TWEEDE DEEL (in the library of Utrecht, now Fortis) and identical tables with an English intro (as our copy) can only be explained, when Vlacq left a number of copies of the tables then in print to Den Decker. He decided to have those offered by Rammensein, the same bookseller Vlacq used for the 1628 Latin and French editions, with a Dutch introduction in 1827. This Dutch version cannot have been too popular. The majority of scientific communication was in Latin in those years. Civilized people being able to afford a book mostly spoke French (and Dutch with their personnel). On top of that Rammensein had to serve two authors no longer on speaking terms with eachother, and it would not be amazing, that he paid more attention to sell Vlacq's Latin and French editions (1000 copies, almost all sold by the end of 1628) than the Dutch edition of the looser Den Decker. Ultimately it evidently was decided to sell remaining copies off to Miller, who issued them as this copy. Detail comparison of type shows many similarities between this copy and the 1628 Vlacq editions (4776-80 errata slip on C5verso, Num. variations). However there are also some striking differences (location of B2 signature), indicating, that the Dutch subtitle copies come from a different (and that can only be earlier) printrun from largely the same type. From this printrun copies are also found with a Latin preface (see Henderson p. 56) and without any text (the UCL copy presented to them in 1861 by De Morgan, and still there).

The Table of Latitudes only occur in the Miller imprinted copies. Note however, that also copies of other printruns must have been sold to Miller: Henderson (p.58) mentions, that the copy of the British Library has no descriptive title to the table of logarithms of numbers (like in our table with French text, book 23165). Also the English introduction can be found bound to a complete Latin edition (Michael Thompsons book 12082). The content of the errata is identical to those in the TWEEDE DEEL. some details in the type show they are newly set however, also adding English text and errata to the trigonometrical tables (not occurring in the TWEEDE DEEL. 10 copies described in COPAC, of which only one [UCL, the Graves copy] mentions those errata.

PROVENANCE:

Turner collection, its bookplate at ffep.

OTHER REFERENCES

Henderson 26.0 states: no errata list is given [see p. 58]. Fletcher mentions the Vlacq 1628 table only, referring for further information to Henderson. Tomash B253 [without any tables]. Only 1 copy in NCC [Delft]. 21 copies in COPAC, not all complete. OCLC mentions 5 copies in US libraries; none of those descriptions mentions the errata present in our copy. € 7.500,00

SOME EXAMPLES OF POPULAR 7 OR LESS DECIMAL TABLES

[012890] Ozanam. TABLES DE SINUS TANGENTES ET SECANTES ET DES LOGARITHMES DES SINUS ET DES SECANTES & DES NOMBRES DEPUIS L'UNITE JUSQUES A 10000. Paris: L'Auteur et Estienne Michallet, 1685. First Edition. (4), 120, (380) pp. Contemporary calf with gilt decorated spine. Edges sprinkled red. Head and tail of spine expertly repaired. Ffep renewed. Inkstain at loweredge, nor showing at pages. With 10 year Privilege du Roi dated 22 March 1685.

Contains logarithms of numbers 1-10.000 to 7 decimals. This table and the trigoniometrical table are taken from Vlacq. this is indicated in the 1697 reprint, which lacks however the goniometrical introduction (120 p.) included in this 1685. Henderson 52.0, not in Fletcher. Tomash O64. € 400,00

[002679] Wolff, Christian. NODIGE TAFELEN TOT DE TRIGONOMETRIA EN UITTREKKING DER WORTELEN WAAR IN DE SINUS EN TANGENTES VOOR ELKE MINUUT DES QUADRANT NEVENS HARER LOGARITHMI…. Amsterdam: Janssoons Van Waesberge, 1742. (18), (92), (2), 95-301 pp. Page 127 and 128 used double. 1 folding plate. The Epkema translation (first impression). Contemporary vellum with handwritten title on spine. Later? red leather label with title in gilt on spine. Red and black title, frontispice engraving. Some contemp. Writing and stamp on title.

Contains log sin log tan, log 1-10.000, squares 1-1.000, sin tang. The logs in 7 decimals, the goniometric tables for every minute. In the same year also a latin edition with the same publisher, which lacks however the squares, and with Vlacq as author. Also in the same year the second edition of Wolff's Mathemetisches Lexicon, including (more elaborate, see Henderson 72.0) tables in a Zweiter Theil (not in 1st of 1716), which Epkema evidently used as a source. Wolff mentions the Vlacq 1628 tables as the most accurate. 4 in PICA. Not in Henderson and Fletcher. Not in Tomash € 400,00

[023326] Vlacq, A.. TABULAE SINUUM, TANGENTIUM ET SECANTIUM, ET LOGARITHMI SINUUM, TANGENTIUM, & NUMERORUM AB UNITATE AD 10000. Amsterdam: Janssoons Van Waesberge, 1742. 48, 283 pp. Original trade cartboards with grey paper spine. Title on handwritten label on spine.

In the same year this publisher issued also a 1st Dutch, edition, which has an identical table of the logs of numbers in 7 decimals (on p.184-283). On the preceeding pages is a combined table of the goniometric values and their logs, as mentioned in the title for every minute also in 7 decimals. In the Duch edition the logs are in a separate table. Not in Henderson and Fletcher. Not in Tomash. € 100,00

[023174] Callet, M.. TABLES PORTATIVES DE LOGARITHMES. Paris: Didot, 1783. First Edition. VI, (7)-64, (522) pp. The unpaged tables collating A3 B-O6 italic A-Gg6. Henderson 85.0, not in Fletcher. Tomash C14. € 250,00

[033619] Hutton, Charles. MATHEMATICAL TABLES: containing the common, hyberbolic and logistic logarithms : also, sines, tangents, secants and versed sines, both natural and logarithmic, together with several other tables useful in mathematical calculations.. London: G. G. J. Robinson and R. Baldwin, 1785. First Edition. XII, 176, (344) pp. Contemporary calf with title in gilt on spine.

The inexactness of the 5th edition of the Sherwin tables inspired Hutton to reduce the number of errors by comparing existing tables of Briggs, Vlacq Gardiner and others. The logaritms 0f numbers to 100000 are given to 7 decimals, however there are subtables giving 20- and 61-decimal logarithms of selected numbers. Trigonometrical tables are to minutes. 160 pages of introduction give a detailed account of the history of tables. On pp. 48ff. an English translation of the descriptive part of the 1624 Kepler tables. Henderson 88, Fletcher p. 404. Tomash H 193. Only 1 copy in COPAC (BL). 3 copies in NCC. € 1.100,00

[023186] Lalande, Jerome De. TABLES DE LOGARITHMES POUR LES NOMBRES ET POUR LA SINUS. Paris: Mme. Ve. Courcier, 1818. 27, (207) pp. 130*80 mm. The tables bound in 6es numbered 1-17. Nouvelle édition revue par M. Reynaud. Publisher ads on p. 4 mention a 3rd edition of Trigonometrie rectiligne et spherique, 3rd edition (1818) for 3 Fr., the next entry being: Les Tables de Lalande sans la Trigonometrie se vendent séparement 2 Fr. The present copy must be of this edition. Contemporary halfcalf with even brown boards. Bookplate on fpep, very small handwritten contemp. name on ffep. Edges stained green.

Small 5 decimal table of logarithms of numbers 1-10.000 and 4 goniometric functions exact to the minute. BNF copy has slightly different collation calling the size 18mo. Later editions at Didot are stereotyped. Not in Henderson and Fletcher. Tomash L14 [a 1802 Didot edition] € 200,00

ANTI-LOGARITHMS

[023444] Dodson, James. THE ANTI-LOGARITHMIC CANON. London: Printed for James Dodson, 1742. First Edition. (4), X, 84, (306) pp. Quires of unnumbered section marked A to Hhhh, last being 1 page. Contemporary calf with illegable title on spine. boards heavily rubbed, hinges broken and loose. Minor browning of pages, some quires mildly foxed.

Dodson's table is by far the most extensive table of anti-logarithms which has been published, and it was practically the first such table in the Briggsian system, if we except the very small table of Long. (Henderson p. 166). Dodson (p. IX) also mentions Long, saying the table (in Phil. Trans 339 (1714)) to contain: ...only of 72 Logarithms of this our table of 100.001 such Logarithms. Dodson further presents quite an interesting bibliography of tables published in Europe untill 1742. In 1627 he mentions: Adrian Vlac published in Goudae in his Trigonometria Artificialis the logarithms of all numbers from 1 to 100.000 and of the Sines and Tangents of degrees and minutes to 10 places of figures. The explanatory part (being an abridgment of Gellibrands Trigonometry) was printed in Dutch, French and Latin; and a second edition of the same in 1628. Indeed in 1627 an edition is known, however with Dutch text, and under the title TWEEDE DEEL DER NIEUWE TELKONST, stating Ezechiel de Decker as author. Of this only a few copies survive (which do not include the values of trigonometric functions; indeed the log-tables in those copies are of the same type as the 1628 editions. Dodson also mixes up titles, the title he mentions actually belonging to a 1633 Vlacq edition. Tables of anti-logarithms give the numbers corresponding to all logarithms, in this table detailed to 11 figures (10 decimal places). It is the 1st table of anti-logarithms, of which this is the only edition. Only in the beginning of the 20th century new tables were issued, Dodson being the only available for over 159 years. Dodson was the great-grandfather of Augustus de Morgan (see his Arithmetical Books p.71. Henderson 201.0, Fletcher p. 390. Tomash D60. 7 copies in the British libraries (COPAC), 1 in LoC. € 2.550,00

FIRST TABLES AT 1” INTERVAL

[023249] Taylor, Michael. Tables of logarithms of all numbers, from 1 to 101000; and of the sines and tangents to every second of the quadrant ... With a preface and precepts for the explanation and use of the same, by Nevil Maskelyne, F.R.S. Astronomer Royal. London: Buckton for F. Wingrave, 1792. First Edition. folio, (16), 64 pp., (446) pp. Tables. Few prefatory leaves bound out of order. Printed on fine thick paper. Contemporary half calf, rehinged. FIRST EDITION of this important set of tables by Michael Taylor (1756-1789), who was a mathematician for the Nautical Almanac; with preface and text by the eminent English astronomer Nevil Maskelyne (1732-1811), who succeeded Bliss as royal astronomer. The next great advance on Vlacq's Trigonometria artificialis took place more than a century-and-a-half afterwards, when Michael Taylor published in 1792 his seven-decimal tables of log sines and tangents to every second of the quadrant: it was calculated by interpolation from the Trigonometria to 10 places and then contracted to 7. On account of the great size of this table, and for other reasons, it never came into very general use. (Encyclopedia Britannica). Poggendorff II, 1072, Henderson 92.0, Fletcher p 436. Tomash T17.

Contains an interesting list of aprox. 400 subscribers, including Callet and Delambre in Paris, von Zach in Augsburg and Bolton in Birmingham. Vlacq (1633) and Ursinus (1624) have an 10" interval, to which Taylor's 1" is a dramatic improvement. Von Zach owned a Ursinus copy (our book 23462), which is amazing as the natural logarithms calculated by him were replaced by the decimal system (log 10=1) after completion of the 1628 Vlacq tables. Briggs and Napier discussed this transition already in 1616, Napier agreeing that a decimal system was more practical for calculation purposes than the natural logarithms introduced by him in 1614. Possibly Von Zach used Ursinus to check calculations prepared using Vlacq. Those new Taylor tables must have been a great help to him. € 800,00

DECIMAL INTERVAL OF THE CIRCLE

[033620] Borda, Ch. Delambre J. B. J.. TABLES Details: Tables trigonométriques décimales, ou Tables des logarithmes des sinus, sécantes et tangentes, suivant la division du quart de cercle en 100 degrés ... précédées de la table des logarithmes des nombres depuis dix mille jusqu'à cent mille . Paris: L'imprimerie de la Republique, 1801. First Edition.

Fletcher p. 379. Tomash B217. 3 in COPAC € 400,00

FIRST CALCULATION LOGS 100.001-200.000

[033793] Sang, Edward. A NEW TABLE OF 7-PLACE LOGARITHMS OF ALL NUMBERS FROM 20,000 TO 200,000. London: Layton, 1871. First Edition. XVIII, (2), 365, (3) pp. Original halfleather with brown buckram boards. Decorated endpapers. Electrotyped (see verso of title). First table to mention this process invented around 1830, and since used for over a 100 years. PROVENANCE: Turner Collection, its bookplate at fpep.

Henderson 174.0, Fletcher p. 112. Not in Tomash. No copy in NCC. 5 copies in UK (COPAC) and 5 in US (OCLC) libraries. Reprinted in 1883 (improved) and 1916 (from the 1871 electrotyped plates now in the custody of the Royal Society of Edinburgh). Henderson also mentions a 1878 reprint, of which no copy can be located however. First table to give the logarithms of the numbers 100.001-200.000, which were recalculated all afresh. Logarithms of lower numbers are from Vlacq (1628). € 450,00

FIRST MACHINE CALCULATIONS

[023208] Bauschinger, J. and J. Peters. LOGARITHMIC-TRIGONOMETRICAL TABLES WITH EIGHT DECIMAL PLACES containing the logarithms of all numbers from 1 to 200000 and logarithms of the trigonometrical functions for every sexagesimal second of the quadrant under the patronage of the Royal Prussian Academyof sciences of Berlin and the imperial academy of sciences of Vienna. Leipzig: Wilhelm Engelmann [Lemcke & Buechner, New York, small stamp on title of volume 1], 1910. First Edition. Two Volumes, 1911 on the title of volume 2. XV, 367, [1] and [II], 951, [1] pp. Numbered 250 and 251, printed on title and by hand on the next page (so this is set 125). B/w frontispiece of a Herr Hamann of Berlin-Friedenau calculating machine facing the title of volume I. Original gray cloth printed black, purple and red print eps, marbled edges. 4to. PROVENANCE: Dudley Observatory, NY, its bookplate at fpep of both volumes. Spine numbers, small ink spot on volume 2.

Built on works of Briggs' Arithmetica logarithmica (Londini 1624) and Briggs-Gellibrand's Trigonometria Britannica (Goudae 1633) and with Bremiker's 6-place table, Bruhns 7-place table, Thesaurus of Vega and Callet's Tables portative de logarithmes. The tables were hand-calculated from the beginning of the work in 1904 until the 1909 delivery of the (pictured) calculating machine which were then randomly checked to 16 places! mostly with complete accuracy. The first tables in the preparation of which major input came from a mechanical calculator. Also for those tables the 18th century Dutch tables were used as a starting point. A 4th edition was published in 1970 and a few years later the tables were superseeded by pocket calculators (my present one calculates 9-digit logarithms in a split second. Henderson 197.0., Fletcher p. 112. Tomash B115. € 450,00

[043872] Peters, Prof. Dr. J.. ZEHNSTELLIGE LOGARITHMEN VON 1 BIS 100 000. Reichsamt für Landesaufnahme, 1922. XVI, 607, (1), XXVIII, 195, (1) pp. Original black quartercloth with brown marbled boards.

Henderson 199.3, Fletvher p. 112. Not inTomash. € 100,00

BABBAGE RELATED EDITIONS

[023146] Callet, F.. TABLE OF LOGARITHMS of sines and tangents, for every second, for the first five degrees, and sines, cosines, tangents and cotangents for every ten seconds of the quadrant. . Paris: Author, Stereotyped and Printed By Firmin Didot, 1827. a-u8 v-y8 z2, 186 leaves, unpaginated. Printed on yellow paper. Leaf 255 x 155mm untrimmed. First and last leaves foxed. Original grey boards with printed paper spine label 'SINES AND TANGENTS TO BABBAGE'S LOGARITHMS', grey sugar-paper endpapers. Slightly rubbed.

Provenance: inscription on rear endpaper 'Mr Jo Scott 10th March 1830'. The logs of sines and tangents from Callet's tables of 1795, re-issued in London to accompany the first edition of Babbage's Table of logarithms. There is no internal evidence that the two were issued together, and the Babbage is often found on its own, but the printed paper label on this fine copy in original boards, reading 'Sines and tangents to Babbage's logarithms' makes the joint issue clear. Furthermore Babbage's innovation of having his log tables printed on yellow paper is used in both books. The book is also advertised in the 1832 edition of Economy of Machinery and Manufactures, together with the Babbage tables of logarithms of natural numbers, which definitely establishes the link. Callet's Tables portatives de logarithmes des nombres depuis 1 jusqu' .. 108000; les logarithmes des sinus et tangentes (1795), is one of the most important sets of tables ever published setting a new standard for accuracy and presentation, and it was the first to be stereotyped, ensuring that figures could not be changed inadvertently in the standing type.

The title states this copy to be 1795-(tirage 1827). Babbage took Callet's table of logarithms as the starting point for the laborious process of checking and collating that went into his own tables (it was this labour that started Babbage's quest for mechanical calculation). The use of coloured paper was one of the many aspects of the presentation of tables considered by Babbage and described in the preface to his Table of logarithms (1827, p. xi): Coloured paper is more favourable to distinctness than white. I had a page set up, and printed on paper of various colours and shades .. Yellow appeared to have the preference, and it is that which I have chosen for the first impression. The tint is at first considerably too deep, but it fades on exposure to the light: I should therefore recommend, that previously to binding this volume the sheets should be exposed for several days to the action of the sun.

Fletcher p. 142. Tomash C16. Gaskell 30/19 (this copy). 4 copies in COPAC and 5 in US libraries (OCLC). Not in NCC. € 5.000,00

[043917] Babbage, Charles. Table of the Logarithms of the Natural Numbers from 1 to 108000. London: B. Fellowes, 1831. Stereotyped-second edition. Collation: [a8] b2 B-N8 O6. 8º (245 x 148mm). Printed on heavy grey paper. A copy on heavier paper than this is not known. Occasional ink splashes. Contemporary maroon morocco (rebacked, inner hinges strengthened, extremities rubbed). PRESENTATION COPY, title inscribed: 'To the library of the Equitable Society from the Author', with a tipped-in 1p. letter from Babbage, 8vo. [folded in 2, the 2nd leave blank], dated Dorset Street/ Manchester Square 30 Nov 1831, stating: I was quite unaware that my little volume on life insurance had not been presented to the Equitable Society. Allow me to redeem this inattention by offering to the Directors two copies of a volume of logarithms .....

The second copy presently is in the library of the Institute of Actuaries [a copy on less heavy yellow paper]. Henderson 130.0., Fletcher p. 375. Tomash B55. PROVENANCE: Christies 6952/40, from the bankrupt estate of Equitable. Copies on yellow and fawn paper are offered in the publisher ads to our book 23147, stating "non stereotype", which is denied by the present copy. € 15.750,00

In the library of the Institute of Actuaries at Staples Inn [London] is a copy of the same edition of those tables with the following dedication:

This copy is printed on yellowish paper, that is about half as thick as that of the grey paper copy. It could very well be the second copy mentioned by Babbage in his letter to Equitable Society. It does not seem quite sensible to have 2 copies of the same title in its library, and thus the secons copy could have gone into the personal library of its director, William Morgan. Large parts of this library after his death were acquire by the Institute of Actuaries.

Babbage experimented quite a lot with paper of different colours. The most extreme example of such experiments is the following copy in the library of the Institute of actuaries:

Some colours are quite heavy, and Babbage recommended to expose them to sunlight to fade. Indeed this type of paper can fade considerably under sunlight even in a few days. Maybe it should be considered to confine this book to the cellar of the Institute in order to retain the still heavy colours on the edges.

[023148] Babbage, Charles. Table of the Logarithms of the Natural Numbers from 1 to 108000. London: John Murray, 1844. (4=blank), xx, 202, (2=blank) pp. stereotyped, fourth and last reprint, tall octavo, contemporary polished calf, contemporary marbled endpapers. Bookplate of Robert Edward Gardiner at fpep, his neatly handwritten name and 1892 on first blank. Contemporary small and neat name and Edinburgh 1852 on title.

An excellent tall copy, all editions are very rare in commerce. Only 1 copy of this (the only Murray) edition in COPAC (UCL). An unchanged reprint of the 1827 (see dating of introduction) stereos. COPAC further mentions 2 1827 copies and 7 other reprint copies.

Henderson 130.0., Fletcher p. 375. Tomash B58.

Babbage closes the introduction with January 20, 1827--Devonshire Street/ Portland Place. In 1832 he evidently has moved and gives Dorset Street/ Manchester Square as address. This key book was a major effort to print in stereotype - for protection against errors - a really accurate set of the logarithmic tables. Babbage was obsessed by the need for such accuracy and was concerned that such tables should be easily and accurately read. It was the necessity to mechanise calculation for tables that were totally accurate that was the major impetus to Babbage's construction of the Difference Engine. The idea of a machine to perform calculation and tabulation automatically was a milestone in the history of computing. It took to 1910 however (the Bauschinger/Peters tables) before computing machines were actually so used. An earlier stereotyped mathematical table is Vega 1825, its 6th edition. See 23198. € 2.625,00

THE VEGA EDITIONS

[023198] Vega, Georg Freyherrn Von. LOGARITHMISCH-TRIGONOMETRISCHES HANDBUCH. Leipzig: Weidmann, 1825. XXIV, 272 pp. 250*170 mm. Sechste Auflage oder erste Stereotypen-Ausgabe. Vega died in 1804, this edition edited by G. Reimer with his 1-page Vorbemerkung. Contemporary halfcalf with gilt title and decoration on spine. Dark brown boards. Some wear and rubbing. Inkstains on title and 3 pages. Name on fpep inked out. 7 decimal logs of numbers (1-100.999) and goniometric functions (sin, cosin, tan, cotan). The first with a German, the second with a German/Latin subtitle. All table pages with Latin headings.

The first 2 tables of Henderson 101.0, LT Tafeln, the collation of the 1st table being in exact agreement. The interesting feature of this edition is that it is the first stereotyped. In this aspect it preceedes Babbage (1827) by 2 years. No such edition in KVK, closest being 1828 8. und 3. stereotype-edition, with identic collation in description. Carter (ABC for Bookcollectors) states, that after improvements by Lord Stanhope in the 1800/1820 period stereotyping became more common. Of which here an early example. The latest edition I have seen is the 85th. edition (1914). Reimer (the editor) remarks in the preface, that the previous edition of 8000 copies was sold in 4 years. The table thus became increasingly popular, and in total maybe not much less than 1 million copies were sold over more than 100 years. Fletcher p.440, Henderson 103 (who did not see a copy of this edition). Reimer mentions in the introduction to this 6th edition, that this is the first edition in which the Latin texts are omitted (earlier editions having a parallel German/Latin text). € 1.200,00

[043822] Vega, Georg Freyherrn Von. LOGARITHMISCH-TRIGONOMETRISCHES HANDBUCH. Leipzig: Weidmann, 1842. XVI, 325, (3) pp. 240*150 mm. Dreiundzwanzigstezigste Auflage.

This edition is the first edited by Dr. J. A. Hülsse with his 2-page Vorrede. Contemporary brown boards. Some wear and rubbing. 7 decimal logs of numbers (1-107.999) and goniometric functions (sin, cosin, tan, cotan). € 200,00

[043821] Vega, Georg Freyherrn Von. LOGARITHMISCH-TRIGONOMETRISCHES HANDBUCH. Leipzig: Weidmann, 1856. XXXII, 575 pp. 220*140 mm. Vierzigste Auflage.

This edition is the first edited by Dr. C. Bremiker with his 10-page Vorwort. Contemporary brown boards. Some wear and rubbing. 7 decimal logs of numbers (1-100.000) and goniometric functions (sin, cosin, tan, cotan). € 200,00

[043812] Vega Bremiker. LOGARITHMISCH TRIGONOMETRISCHES HANDBUCH. Zürich Berlin: Weidmannsche Verlagsbuchhandlung, 1964. X, 570 pp. Original grey cloth with title in black on frontboard and spine. 101. Auflage, the last known to me.

Note, that log tables became obsolete after inexpensive pocket calculators became available in the mid-seventies. 7 place logs of the numbers 1-100000 and of sin and tang with a 1 second interval (a Bremiker innovation). Early Vega tables are at a 1' interval, giving also 10" details for the first 6 grades. € 100,00

AND ANOTHER POPULAR GERMAN TITLE

[023192] Kohler, Heinrich Gottlieb. LOGARITHMISCH-TRIGONOMETRISCHES HANDBUCH. Leipzig: Bernard Tauchnitz, 1898. XXXVI, 388 pp. Sechzehnten Stereotypausgabe, the last edition. Contemporary halfcalf with gilt title on spine. Sprinkled edges. Calf heavily rubbed, front hinge open but strong, edges rubbed. 7 decimal logarithms of 1-100.000, 8 of 100.000-108.000.

The table is in "modern" format, omitting the first 3 decimals, when they are identical. This format was introduced by Babbage in 1827. Further the logs of goniometric values at 7 decimals and many other tables and log-values. First published in 1847, second (1848) with substantial corrections is considered the definitive version (= Henderson 151.0. Henderson and Fletcher (p. 408) both quote the 16th edition as the last. The first stereotyped German table in a quite rare and interesting edition. € 100,00

No copy of any of those 5 in Tomash.

TRIGONOMETRIC TABLES ONLY

[023166] Briggs, Henry and Henry Gellibrand. TRIGONOMETRICA BRITTANNICA. Gouda: Rammaseins, 1633. First Edition. (8), 110, (2=the blank O4), (272) pp. 324*190 mm. Contemporary calf with gilt title on spine. Marbled endpapers. Edges with gold decoration, page-edges stained red. Bookplate of Marquis de...(name erased)on fpep. Minor waterstain on last 5 pages. Some pages shortly cut, resulting in (partial) loss of title (consisting of degree number only) on 50 out of 90 versos. Corrected last column (and the relating instruction) glued to recto of F3. An identical instruction is included in the errata (see last unnumbered page in front). The corrected last column was possibly printed on the blank O4, which misses a corresponding amount of paper at the foreedge. Collation agrees with the description of the copy in Oxford.

This is the first edition of goniometric tables (including their logarithms) calculated by Briggs and edited by Gellibrand after his death. The tables are detailed in degrees and 100 decimals per degree. The number of decimals calculated is: sin (15), tan (10), sec (11), logsin (14), logtan (10). The detail is extremely high, and especially for sin and logsin unsurpassed in any later calculations. Never reprinted. In 1946 Fletcher writes: Perhaps only Briggs/Gellibrand 1633, which has never been equalled, ...is still of great working value (p. 4) and: A new edition of Briggs and Gellibrand is badly needed (p. 124). In 1628 Vlacq already included only the logs (10 decimals, in comparison with Briggs detail relatively easy to calculate) of goniometric values in his Arithmetica. Honeyman 506. Fletcher p. 380. Tomash B 256. Oxford (collated) and 6 uncollated copies in COPAC, 6 in PICA.

BOUND WITH:

[023167] Vlacq, Adrian and Henry Briggs. TRIGONOMETRIA ARTIFICIALIS. Gouda: Rammaseins, 1633. First Edition. (8), 52, (408) pp. 324*190 mm. BOUND WITH: Trigonometria Brittannica (1633). For description of binding see our book 23166. Same size as that book, however in this title no text shaved. Browning, 5 leaves quite heavily.

In this volume Vlacq publishes in first edition the logarithms (the usual 10 decimals) of goniometrical values at 10 seconds detail. In Arithmetica (1628) the detail was to minutes. It further includes the logarithms of the figures 1-20.000 unchanged from the 1628 edition, and without correcting the errata. Also signatures and a correction pasted in at the verso of C5 are identical to the 1628 edition. In the quires E and F the column-headings Num. show an identical variance of the full stop, sometimes missing and sometimes printed higher. Therefore those sheets could even come from the same 1628 printrun. A very important table, the first to 10" detail (Brittannica being detailed to 100 minutes in a grade). Only in 1792 the Taylor tables to a 1" detail were published. This Vlacq table was one of the source tables of Vega's Thesaurus (1794), itself the basis for many editions of 7-decimal tables. Up to the end of the 19th century millions of copies of those were printed in Germany.

Fletcher p. 440. Henderson 31.0. Tomash V12. 1 copy in COPAC (UCL), of which the description states 5 beginning leaves (our copy 4, being halftitle, title, adress and praefatio). 3 copies in PICA.

€ 6.000,00 together with Brittannica.

ASTRONOMY

[064170] Halley, Edmund. CATALOGUE DES ESTOILLES AUSTRALES. Paris: Jean Baptiste Coingard, 1679. [32], 118, [2] rare foldout plate [with fig. I-IIII] tipped in at fore-edge of rpep. *6 **6 ***4 a-k6. k6 is blank. It has a quite typical watermark also occurring in i6. 12mo in sixes, 137* 78 mm.. Contemporary calf, partial title and decoration in gilt on spine. Edges decorated in gilt, edges of pages sprinkled in red. PROVENANCE: A.J.P.C. Duc de Lachapelle ex lib. of his observatory at Montauban, 1785, see contemporary handwritten note in ink at ffep. Textpages annotated in contemporary ink with astronomical observations. Outer hinges professionally repaired. Text in Latin and French, the title however in French only. FIRST EDITION IN FRENCH, second in Latin, published the same year as the first Latin edition.

Halley was the first European scientist observing the stars of the southern hemisphere. For this sole purpose he travelled to St. Helena in 1677 [see also p. 1]. It is the first astrometric catalogue with the new telescopic instruments (Cook, Halley, p.413); on the basis of its publication at London, Halley was elected member of the Royal Society. As stated in the preface, Halley's catalogue was published just as the last page of a star catalogue by Auguste Royer came off the press (Cartes du ciel, Paris: Coignard, 1679) and so it was decided to print Halley's work in French translation too. Despite the editor's reference to it being comme une seconde partie au nostre, the two works are independent publications and survive more often individually than joint. Cook (Halley pp. 78 and 463) identifies the translator as van Luer, and calls for the planisphere to accompany the text; it is not present here, nor in the Macclesfield, Royal Astronomical Society, British Library, or the two Paris Observatory copies. Furthermore, the engraved plate with 4 figures -- present here -- is lacking in all those noted above except a British Library copy.

The volume's former owner, Duc de Lachapelle, was a serious amateur astronomer. He built his own observatory at Montauban and some of his astronomical observations were published in Connaisance des temps; he was elected an associate member of the Académie des Sciences in 1796.

Thanks should go to Françoise Launay for her assistance in investigating this edition and its copies in France. No copy in NCC and OCLC. The only other copy known to include the foldout plate in the rear is in the British Library [London]. 10 other copies without plate in the UK [3], France [5] and Germany [2], some having 1 or 2 blank leaves after ***4. The introduction further mentions on **6 recto a planisphere, which is not present in any copy known however. € 8.500,00

[033797] Halley, Edmund. ASTRONOMICAL TABLES. London: William Innys, 1752. First Edition. Unpaginated. At the end of the book is a Registrum stating the signatures to be present (signed corrig. in a contemporary hand). Those quires are present except * and (a) in the beginning of the book. Instead: unsigned 1 (Privilege on verso), frontispiece portrait of Halley (facing title), title, halftitle, A2 (Preface), unsigned 2 (1st 4 pages of Precepts for using the Tables). At the rear of the book there are an additional leave of Errata and 2 leaves of index. Contemporary calf with title in gilt on spine. Worn and shaved, the hinges skillfully repaired. PROVENANCE: John Smith, 1770 (handwritten statement of ownership on fpep. Turner Collection, bookplate at ffep. € 3.000,00

[084280] ZACH, Franz Xaver, Freiherr von.. Tabulae Motuum Solis Novae et Correctae ex Theoria Gravitatis et Observationibus recentissimis erutae. Quibus accedit Fixarum praecipuarum Catalogus Novus ex Observationibus Astronomicuis Annis 1787, 1788, 1789, 1790 in Specula Astronomica Gothana Habitis. Gotha: Ettinger, 1792. Engraved frontispiece giving two views and the floor plan of the observatory at Gotha. [8]. 195, [1], CCL pp. Large 4to, Contemporary calf with title and decoration in gilt on spine.

The astronomer Franz Xaver von Zach (Pest 1754) built and supervised the Seefeld observatory for Herzog Ernst II von Sachsen-Gotha- Altenburg in 1788. In the time it was the most modern observatory in Europe, Lalande made a vist in 1798 (Brosche p. 88) and Gauss in 1803. After the death of Ernst II in 1804, Zach was quite involved in assisting his widow. In 1806 he renounced his position with the observatory to accompany her on her travels thru Europe. 1800-1813 he edited the MONATLICHE KORRESPONDENZ ZUR BEFORDERUNG DER ERD- UND HIMMELKUNDE, one of the first scientific journals. Zach died in 1832 in Paris. Zach is not too well known nowedays. However: The history of astronomy and exact geo-sciences of the Goethe era cannot be written, when Zach is ignored. (Peter Brosche, Der Astronom der Herzogin, Leben und Werk von F X von Zach, Frankfurt am Main, 2001, the last sentence of the introduction). Brosche argues, that nevertheless Zach's role as a catalyst and scientific manager is not easily seen by a lay public focussed to the end products of the scientific process only. Brosche (p. 256) mentions 41 crates of books shipped by von Zach when moving from Genua to Frankfurt in 1827. € 850,00

PRIMES

[023578] Marci, Adolf Frederik. UITVOERIGE TAFELEN VAN DE ONDEELBAARE OF PRIM-GETALLEN. Amsterdam: J. Morterre, 1772. First Edition. 44, 190(tables), (2) pp.8to (210*120 mm), table however bound in fours. Contemporary halfcalf, spine gilt with morocco letterpiece. Modern piece of stiff paper mounted on lower pastedown. Boardedges worn; paper over boards rubbed. Marci translated the Wolff, Principles of Mathematics (1742) and futher a description of the Amsterdam townhall is known from him. His actual position in 18th century mathematics is not clear however; Bierens de Haan mentions: Maitre dárithmetique, teneur de livres et translateur à Amersfoort et Amsterdam; décédé 1774, and mentions in total 6 titles. Rare early table of prime numbers.

Not in Fletcher (the earliest tables he mentions are Lambert 1770 (to 101977) and Vega 1797 (102000-400031). Both tables together thus miss 101977 and 101999 given by the Marci table as primes. Bierens de Haan 3013. Not in Tomash. 2 copies in NCC (Leiden and UvA). Not in COPAC and KvK, which explains the Fletcher omission. OCLC mentions no copies in US libraries. € 500,00

INTEREST

[012903] Smart, John. TABLES OF INTEREST, DISCOUNT, ANNUITIES, &C.. London: 1726. First Edition. (10), 123, (1) pp. 4o. (265*206). Large and heavy paper copy. An earlier table was published by Smart in 1707. That is in 8o however and has only 72 p. Annuities (the most interesting part of this title, also quoted by Pearson) and some other sections of the present edition were not included in 1707, and thus are here in first edition. General printed dedication to the Governor, Deputy-Governor and 24 Directors of the Bank of England on A2 following title. Contemporary English red morocco gilt in the Harleian style, gilt central cartouche on covers with broad dentelle within a double fillet, spine with gilt decoration and title in six compartments, gilt edges of boards. Contemporary marbled endpapers. All edges gilt. Professionally rebacked retaining spine and reinforcing hinges). With first blank and halftitle Errata on verso of contents.

PROVENANCE: Similar copies (binding, paper and dedication) are described by George Baytun (catalog1#72 and also book #ebc603). Also Heritage #39526 (the Kenney copy). It therefore looks like Smart had 26 identical copies made for the board of the Bank of England. One could argue, that this is a unusually large number of bespoke bindings, or go with Bennett and call it a deluxe publishers binding. Smart's tables were often copied unquoted or quoted (see for instance Baily (1808) book # 12901 and thus stayed in use for over 150 years. Mr Smart is very strict on annuities. Therefore his table on page 114/15 only give the number of years and days to reimburse the annuitant their purchase money, for interest rates from 2-10%. He feels that in his time the recording of the age of persons died was not recorded relyably by the parish clercks. One year after the publication of De Moivre's annuities (which use the 1690 data of Halley) I hear some critique here. Smart sternly closes this chapter saying: and this is all I shall say with respect to Annuities upon Lives. Kress 3666. Tomash S 127. € 600,00

[023440] NEWTON, Isaac (Sir).. TABLES FOR RENEWING AND PURCHASING THE LEASES OF CATHEDRAL CHURCHES . London: Thomas Astley, 1742. Continuation of title: ...according to the several rates of interest: with their construction and use explained. Also tables for renewing and purchasing the leases of land or houses, very necessary and useful for all purchasers, but especially those who are in any way concerned in church or college leases. To which is added, the value of church and college leases consider'd, and the advantage to the lessees made very apparent. By a late Bishop of Chichester. To which are also added, tables of interest exactly computed at 3, 3 1/2;, 4 and 5 per cent, with other useful tables. As usual (see subtitle pocketbook) bound with: THE MONEY'D MAN'S POCKET-BOOK. Being tables of simple interest exactly computed; for one to twelve months Sixth edition. 4, 107, (1); (6),102, (2) pp. 12mo. Modern quarter calf gilt title with marbled boards. Both works signed by Astley, Newton on verso of title and the Pocketbook on th 3rd unnumbered page. Westfall 12. Not in Tomash. € 450,00

[012916] Griffin. INTEREST TABLES. London: Carnan, 1775. First Edition. [344]pp. A2, B-Uu4, Xx2. 8vo. folded in fours. (210*135 mm). Original green vellum-backed boards, printed spine label mostly rubbed away, top of spine torn, sides scuffed. First edition.

An unusual Newbery survival (Thomas Carnan was the stepson of John Newbery). While duodecimos bound in Newbery's characteristic "vellum manner" survive in great numbers, he bound very few octavos in the same style. There is evidence of an old label removed from the front pastedown; we have seen another copy of the same book containing a printed note explaining Newbery's decision to bind volumes in vellum. The bindings are discussed at some length by Michael Sadleir in his Evolution of publishers' binding styles.

Not in Tomash. Scarce; L, C, SAN; MiU in ESTC 1990. Roscoe A204.

€ 500,00

[012901] Baily, Francis. THE DOCTRINE OF INTEREST AND ANNUITIES ANALITICALLY INVESTIGATED AND EXPLAINED with Tables. London: John Richardson, 1808. First Edition. XIV, (2), 144, (2), (60), (2) pp. 1st.ed., 4to.,with the halftitle, tables + errata and binders note, 1 plate, publisher's ads at end, a crisp copy in contempory polished calf, a little wear to upper hinges. Wear at corners. PROVENANCE: John Temple, his bookplate at the fpep.

Very scarce and for the remainder of the century regarded as the definitive word on the subject. Baily worked on the Stock Exchange until his death in 1825 but made a powerful reputation for his writings in astronomy and, as here, on life assurances.

Not in Tomash. € 600,00

[053989] Scientific Computer Service. COMPOUND INTEREST TABLES. Epping: Scientific Computer Service Ltd, 1965. [3], 110. [1] pp. 4to [255*205 mm.]. Original brown leatherette boards and spring binding. Errata slip pasted on beginning of 1st line of preface.

Produced in cooperation with the Institute of Actuaries. From the preface: The layout of these tables is broadly similar to that of those provided for students of the Institute of Actuaries' examinations. Their range, however, is much wider than a mere sample set, and covers the whole ground recommended by the Institute.". For interest rates from 1/8 to 10% with an interval of 1/8 to 1% then 1/4 to 7% and then 1/2 to 10%. For percentages over 1% n= 1 to 100, thereunder n= 1 to 200; 5 decimals. PROVENANCE: Institute of Actuaries, its small stamp on preface. A strip stating "NOT TO BE TAKEN AWAY" pasted to front board. The table data possibly offset from computer output. 1 copy of this edition in COPAC (BL), followed by a reprint in 1966 with identical collation. Thereafter parts of the material was reprinted up to 1978, the year I purchased my first Casio pocket calculator.

Not in Tomash. € 250,00

[013101] Michels, Drs. J J M En Drs. A J Van Reeken. ZES INTRESTTAFELS. Tilburg: Universitaire Pers Tilburg, 1971. First Edition. VII, 308 pp. Original blue and white printed wrappers. Contains intrest tables for 50 periods and percentages from1/8 to 50%.

An extremely large number of tables, enabled by the use of Tilburgs ICL 1903A computer. The dramatically new feature of this edition is, that it is the first manufactured directly from the output of the line-printer, thus eliminating typing errors in the manufacturing process. Improvements in this direction started in 1827, when Charles Babbage made the first table from stereotyped type. Babbage was extremely concerned over typing errors, and indeed succeeded in eliminating errors with the type after typing, however the problem of initial input errors was not solved. Not much changed untill around 1950 punched-card computing systems (developed for bookkeeping oriented purposes were made available for scientific purposes. Tompkins (High-speed Computing Devices, 1950) writes: ...it is possible.... to print tables which can be reproduced by a photo-offset process without any intermediate manual duplication. So evidently that was seen as the next step in 1950. There are some traces of tables being on punched-cards themselves, but so infrequently, that this can have been widely practiced. This is the first "photographic" edition from computer-output I know of. I remember to have used it for complex IRR calculations, for which other tables did not address the wanted percentage, and where also my self-reversing automatic Monroe deviding machine (very advanced in the time!) could not help me. There will not have been many editions: in 1978 my first pocket calculator (at the enormous expense of f 125) made the necessary calculations within seconds. Subsequently the for IRR-calculations still necessary trial and error was eliminated by the corresponding function in Visicalc (1982). The youngest antiquity I know of, and possibly the rarest. Librarians do not love intrest-tables, there is no copy in the Dutch University Libraries. Antiquarians do not fancy tables, and copies turning up in larger lots are likely to end up in the pile "throw away".

Not in Tomash. € 250,00

ACTUARIAL TABLES

[114325] Graunt, John. NATURAL AND POLITICAL OBSERVATIONS MADE UPON THE BILL OF MORTALITY. London, Tho: Roycroft, for John Martin, James Allestry, and Tho: Dicas, 1662. Reprinted in [same title] edited with an Introduction by Walter F. Willcox, The John Hopkins Press, Baltimore, 1939.. XIII, (3), 90, (2) pp. 1 fold out table facing p. 80. Original grey wrappers printed in black.

Graunt is memorable mainly because he discovered the numerical regularity of deaths and births.... In doing so he opened the way for the later discovery of uniformities in many social and vollitional phenomena like marriage, suicideand crime, and for the study of these uniformities, teir natureand their limits; thus he, more than any other man, was the founder of statistics [Willcox closing remark in his introduction. Institute of UK Actuaries [see p. 66] and Utrecht [see p. 681] both have a 1665 Oxford copy, which Utrecht defines as a 4th impression. I of A also states: the same, 1676. 2 copies in NCC [KB and Erasmus]. Even this reprint is rare nowedays. € 607,00

[023505] Witt, Johan de, WAARDYE VAN LYFRENTEN NAER PROPORTIE VAN LOSRENTEN, ’s Gravenhage, 1671. Reprinted in French in: Chateleux, P. J. L. et J. P. Van Rooijen. LE RAPPORT DE JOHAN DE WITT SUR LE CALCUL DES RENTES VIAGERES. Den Haag: Martinus Nijhoff, 1937. First Edition. (4), 45, (3=blank) pp. frontispiece portrait of De Witt. Original grey wrappers with title printed in black. A mint copy, only the pages a bit browned.

French translation prepared for the 11th International Congres of Actuaries held in the year of publication. The Waardye is the oldest publication incorporating calculations concerning financial consequenses of the rate of death of mankind. This, despite all its imperfections makes De Witt the founding father of actuarial science. € 25,00

[114334] Halley, Edmund. DEGREES OF MORTALITY OF MANKIND. London: Royal Society, 1693. Reprinted in: Two papers on [same title] edited with an Introduction by Lowell J. Reed, The John Hopkins Press, Baltimore, 1942..VI, 21, (1) pp. Reprint from the Philosophical Transactions of the Royal Society Volume XVII (1693) # 196 from the copy of the Transactions in the Library of Congress. Also included are some further considerations, # 198 in the same volume. Original grey wrappers printed in black. With facsimile of the title of the volume and the headings of the papers. The text is newly set.

The first document into which an actual mortality table is included, prepared by Halley using mortality data of the city of Breslau prepered by Neumann. First reprinted in: Miscellanea curiosa 2nd ed. London : Smith, 1708 [Vol. 1], p. 280-301, and also in the Journal of the Institute of Actuaries (Volume 1, 1851). However this is the first and only separate offprint. Major libraries have those papers in their complete set of Transactions. This is out of scope however for private collectors, as are the reprints mentioned. As a result there is no copy of those important papers in Norman and Honeyman. However Institute of Actuaries [see p. 70] mentions a seperate 1726 edition and Utrecht [see p. 664] a 1748 edition. No copies of this new 1942 offprint in either of the last 2 collections. The I of A catalogue closes 1935, they will have obtained a copy. It is likely however, that Utrecht [closing 1949] could not get a copy in 1942 due to war circumstances and that the title was sold out in 1945, after the end of the war. € 295,00

[012878] De Moivre, A. ANNUITIES UPON LIVES. London: Francis Fayram and Others, 1725. First Edition. (2), 4, VIII, 108, (2) pp. Errata, sometimes found on P4, are in this copy pasted to VIII. 20th century halfcalf with nicely decorated boards and title in red shield on spine. 5 raised bands. New endpapers. Faint waterstain on lower right corner, a bit stronger on the last 3 leaves. Provenance: P Taylor: his signature on the title, and a pupil of De Moivre.

On the recto of the last leaf Halley’s Table of life, an early reprint. Kress 3595, Norman 1530, RKN 20059, Tomash M113 [in a Sammelband], Israel 112/80 [this copy]. 3 copies in NCC [RUL, VU and Delft.]. Institute of Actuaries p. 39, Utrecht p. 521. € 5.000,00

[054004] Hayes, Richard. A NEW METHOD FOR VALUING OF ANNUITIES UPON LIVES.. London: Printed for R. Hayes, and sold by him and J. Bowles ..., and by W. Meadows ..., and by H. Whitridge, 1727. First Edition. [8], 128 pp. Small 4to [190*160 mm.]. Panelled calf with title on paper label on spine. Quite rubbed, upper hinge neatly repaired by Henk Linde [restaurator specialized in repairs on leather]. Calf foldins causing browning of endpapers. PROVENANCE: Bibliotheek van de Algemene Maatschappij van Levensverzekering en Lijfrente te Amsterdam #98, its stamp on ffep. This insurance company was quite active in the exploration of the history of the insurance business, its director Schevichaven being well known as an author on the subject [see Bouwstoffen [1897], book 23453 in the present collection] . The company bankrupted in 1921. Policies were taken over by companies now in the Aegon-group and other assets were dispersed. This copy was evidently purchased by an insurance company now absorbed in the Hoge Huys-group, which later offered it for auction. Institute of Actuaries p. 74, Utrecht only has the 1746 reprint, see p.41. Not in Tomash. 6 copies in COPAC. € 4.000,00

[043897] Struyck, Nicolaas. INLEIDING TOT DE ALGEMENE GEOGRAPHIE BENEVENS EENIGE STERREKUNDIGE EN ANDERE VERHANDELINGEN. Amsterdam and Paris: Isaak Tirion, 1740. First Edition. (12), 176, 392, (2), 8 pp. In the first part the pages 163*-166* are added and in the second part pp. 299*-302*. There further is no leave Q4, pagination and text being continuous however. Engraved portrait facing title, 9 folding plates and 1 folding table. 4to (265*200 mm). Original contemporary halfcalf trade binding with brown boards, spine rebacked in period style. Some minor foxing. Waterstain in lower white margin of 2nd part. Nowedays the author is best known for his contributions to the actuarial science. His 3 earliest papers on this subject are here included on pp. 321-392 in 1st edition. PROVENANCE: Bibliotheca Didina et Pinguina, see auction slip (Bubb Kuyper 41/13) bearing its engraved logo laid in. Bierens de Haan 4678 and 4679. UK Institute of Actuaries only has the Vollgraff translation in French, Utrecht p. 696. € 3.500,00

[054003] Deparcieux, A.. ESSAI SUR LES PROBABILITÉS DE LA DURÉE DE LA VIE HUMAINE.. Paris: les Frères Guerin, 1746. VI, [2=approbation, avis au relieur and 3 other items], 132, XXII, [1=privilège du roi], [1=blank] pp. Collation: a4 A-Q4 R2 a-m2. 4to [257*198 mm.], representing above average ample margins. Quite heavy paper (100 pp.=9 mm.], as all copies known to me. Contemporary calf with gilt decoration and title in red lettering piece on spine. all edges red. Small label at frontboard. Some wear at head and tail of spine. Quire L a triffle browned, further a very clean and white copy. PROVENANCE; De Noordhollandsche Levensverzekerings-Mij N V, its small stamp at the halftitle. This company was ultimately acquired by De Hooge Huys [Alkmaar], from which the book was purchased in auction. IoA p. 41, Utrecht p. 538. Tomash D42. 1 copy in NCC [Leiden], not in UvA.. RKN 3968. Quaritch 1297/46. Macclesfield IV/613. € 7.900,00

[043880] Kersseboom, Willem. A VIEW OF THE RELATION BETWEEN THE CELEBRATED DR. HALLEY'S TABLES AND THE NOTIONS OF MR. DE BUFFON, FOR ESTABLISHING A RULE FOR THE PROBABLE DURATION OF LIFE OF MAN.. London: Royal Society, 1753. pp. 239-252 of the Philosophical Transactions XLVIII [extracted]. Translation James Parsons. Of all publications of Kersseboom this is possibly the most important one concerning a comparison of the life tables of Halley and Dupré de St, Maur. See further Pearson Lectures p. 188 and further p. 192. More interesting than the Dutch language Proeven from the same author. Not in IoA and Utrecht. € 290,00

[023521] Süssmilch, Johann Peter. Die göttliche Ordnung in den Veränderungen des menschlichen Geschlechts : aus der Geburt, dem Tode und der Fortpflanzung desselben . Berlin: Buchhandlung der Realschule, 1775. First Thus. 3 volumes XX, 576, 130; (4), 580, 81 and XVI, 735, 68 pp. 184*115 mm. New calf with gilt title on spine in burgundy letterpiece.

Süssmilch lived 1707-1767, this edition edited by his son in law Christian Jacob Baumann, who added the third volume, subtitled Anmerkungen und Zusätze, here in 1st edition. Vierte verbesserte Auflage. It should be realised however, that the 1st edition (1741) has as collation: 40. 356, (40) pp. Also in volumes 1 and 2 therefore the majority of the text is added after the 1st edition. PROVENANCE: Freie Universität Berlin (Seminar für Statistik), its stamp and cancel on verso of title and p. 48 (as usual) of each volume. There are 6 other copies of this title in the Berlin area (see KOBV), 4 facsimiles and 2 copies at the Freie Universität, this copy evidently considered to be double. They evidently have a disinvestment program, see also book 12781, like Leiden is presently contemplating (rectoral speetch 2002/03). In other libraries a 1765 (3rd edition)/1776 copy occurs quite frequently (for instance Leiden). the other copy in The Netherlands is a 1798 copy in Groningen. So of this (letzter Hand) edition. No copy in The Netherlands 2 copies in COPAC (UCL and ULL). € 3.300,00

[023413] Morgan, William. THE PRINCIPLES AND DOCTRINE OF ASSURANCES, ANNUITIES ON LIVES AND CONTINGENT REVERSIONS, STATED AND EXPLAINED . London: Longman, Hurst, Reese, Orme and Brown, 1821. First Edition. xvi + 326pp, with erratum on verso of title, contemporary quartercalf with marbled boards, First edition thus (but refer to note below). Although Morgan regarded this as a revised edition of a work 'published above forty years ago' [viz. his Doctrine of Annuities and Assurances, 1779], this is in most respects an entirely new work. As actuary to the Equitable Insurance Society (1775-1830), Morgan has been accorded a leading place among the pioneers of life insurance. He published both papers and substantial treatises on the subject over the greatest part of his lifetime. Kress C.740. Goldsmiths 23216. Cat. of the Library of the Inst. of Actuaries, 1935, p.116. € 300,00

[114326] Gompertz, Benjamin. ON THE NATURE OF THE FUNCTION EXPRESSIVE OF THE LAW OF HUMAN MORTALITY.... London: Royal Philosophical Society, 1825. 513-585 pp. Extracted from Philosophical Transactions volume 115 [1825]. On p. 517 the famous distiction between accidents and deterioration as causes of death. IoA p.65, Utrecht p. 542. € 450,00

[012905] Duncan James J.. TABLES OF THE PROBABILITY AND EXPECTATION OF MALE AND FEMALE LIFE. Glasgow: John Cunninghame, 1829. First Edition. 68 pp. Original brown boards with white sticker printed in black and blue on front board. Boards and ep. with some (water?)damage at edges, hinges expertly repaired and spine renewed. Uncut and partially unopened. The copy includes interesting tables of probabilities of male and female life based on Glasgow records 1821/27. To my knowledge this are the first emperical tables based on sex-stratification. PROVENANCE: Samuel Brown, Equitable, 28 May 1849; his name in contemp. handwriting on fpep. IoA p. 45, not in Utrecht. No reprints known. No copies known in The Netherlands and USA. COPAC mentions 2 copies in the UK: NL of Scotland and Edinburgh. Not in RUL. € 600,00

[012956] Moser, Ludwig. DIE GESETZE DER LEBENSDAUER. Berlin: Veit Und Comp., 1839. First Edition. XXVIII, 399, (1=blank), 2 leaves with 5 fold-out tables. Contemporary quartercalf with brown marbled boards and gilt title on spine. Edges of pages stained green. Lower edges of boards and corners quite rubbed. A clean copy on quality paper, this book will not have any trouble to survive many ages.

The author (professor der Physik at the university in Koningsberg) is one of the first to address mortality in the calculation of pensions and life-insurances. Evaluation of the tables prepared by Kersseboom and by Euler. Also includes evaluations of the outcome of early quantitative population research. Poggendorff II, 215. Humpert, Kameralwiss. 7269. 3 copies in COPAC (2 in BL and Wellcome). 5 in NCC, so evidently in the time well known outside Germany. Institute of actuaries p. 117, Utrecht p. 645. € 700,00

[064122] Farr, William. ENGLISH LIFE TABLE. TABLES OF LIFETIMES, ANNUITIES, AND PREMIUMS.. London: Longman, Green, Longman, Roberts, and Green, 1864. First and only Edition. [4], CLV, [1] =blank, 605, [1] =colophon pp. Royal 8vo [265*185 mm.]. The colophon page of this book indicates that 500 copies were printed. Original diaper black cloth with gilt arms to front cover. Sympathetically rebacked with matching material. Original yellow mat coated endpapers. PROVENANCE: the library of the ecclesiastical commisioners for England, its bookplate at fpep and a stamp 'supplied for the public service' to the title. The English Life Table contains a tremendous amount of data-6.5 million deaths sorted by age. Included in English Life Table no. 3 are the first lengthy working tables produced by the Scheutz printing calculator-the first instance of such a machine being used extensively to do original work. However, none of the hoped-for benefits of mechanizing the calculation of the tables were realized, since the Scheutz machine failed to include any of Babbage"s security mechanisms to guard against mechanical error, and it required constant maintenance. Of the 600 pages of printed tables in the book, only 28 pages were composed entirely by the machine; a further 216 pages were partially composed by the machine, and the rest were typeset by hand. Nor was there the hoped-for savings from using the machine to prepare stereotype plates. Her Majesty"s Stationery Office, printer of the volume, stated that having the machine set the entire book automatically would have saved only 10 percent over the cost of conventional typesetting (Swade 2000, 203-8). Pages cxxxix-cxliv contain Farr"s appendix entitled "Scheutz"s calculating machine and its use in the construction of the English life table no. 3," in which he emphasized the usefulness of the new machine, but also the delicacy and skill necessary for its operation: The Machine required incessant attention. The differences had to be inserted at the proper terms of the various series, checking was required, and when the mechanism got out of order it had to be set right. Of the first watch nothing is known, but the first steam-engine was indisputably imperfect; and here we had to do with the second Calculating Machine as it came from the designs of its constructors and from the workshop of the engineer. The idea had been as beautifully embodied in metal by Mr. Bryan Donkin as it had been conceived by the genius of its inventors; but it was untried. So its work had to be watched with anxiety, and its arithmetical music had to be elicited by frequent tuning and skilful handling, in the quiet most congenial to such productions. This volume is the result; and thus-if I may use the expression-the soul of the Machine is exhibited in a series of Tables which are submitted to the criticism of the consummate judges of this kind of work in England and in the world (p. cxl). Farr also noted Babbage"s contribution to the venture-it was Babbage who "explained the principles [of the Scheutz calculator] and first demonstrated the practicability of performing certain calculations, and printing the results by machinery" (p. xiii). Having invested so much time and money in the project while realizing only token gains, the British government showed little patience with the Scheutz calculating machine. The General Register Office soon reverted to manual calculations by human computers employing logarithms, which they used until the GRO's conversion to mechanical calculation methods in 1911. Institute of Actuaries p. 53, Utrecht S-VI 26 see p. 556, OoC 85, Tomash F18, all this 1864 edition. 1 copy in NCC [UvA], 3 in COPAC [BL, NLS and Edinburgh], OCLC mentions 12 copies in US libraries and another UK copy in Cambridge. RKN 4702. Not in RUL. € 5.395,00

[023453] . BOUWSTOFFEN VOOR DE GESCHIEDENIS VAN LEVENS VERZEKERINGEN EN LIJFRENTEN IN NEDERLAND. Amsterdam and Paris: 1897. First Edition. (8), 370, (2) pp. Contemporary halfcloth with decorated boards. With frontispice portrait of Johan de Witt and 11 other plates on heavy paper. Plates lightly foxed. Edges and boards slightly worn. Chapters on 12 Dutch mathematicians having contributed to actuarial knowledge, starting with Johan de Witt. Originally published in installments by the Algemeene Maatschappij van Levensverzekering en Lijfrente in the circular to its agents in 1887 to 1895, now rearranged by mathematician. The texts are mostly written by S. R. J. van Schevichaven, then a director of the Algemeene (see the introduction to the Collected Works of Struijk, 1912). On p 4-5 a good inventory of copies of WAERDIJE (1671), the 1st document in Dutch applying mathematics to the duration of human life. However in 4 letters written to his brother Lodewijk in 1669 Christiaan Huygens treats the subject quite in-depth. In a supplement there is even a kind of table of probability of human life. Those were not published however before 1897 in Volume VI of the collected works of Huygens. The authors of BOUWSTOFFEN got proofs of that text, and included it on p 64-83. Also included is the complete original Dutch text of VAN REKENINGH IN SPELEN VAN GELUCK (p. 42-62), a very early text on probability, sent by Huygens on 27th April 1657 to Frans van Schooten, and included by him (translated in latin) in EXERCITATIONES MATHEMATICAE (1657). Further original documents included are the TAFEL VAN AFSTERVING of Hudde and 3 Memorien by Kersseboom (here in 1st printing). A very extensive source of early actuarial material rarely found elsewhere. € 60,00

SECONDARY LITERATURE

[023419] Popock, Lewis. A CHRONOLOGICAL LIST OF BOOKS AND PAMPHLETS RELATING TO THE DOCTRINE OF CHANCES AND THE RATE OF MORTALITY, Annuities, Reversions, Marine and Fire Insurances, and Life-Assurance; with the titles of the several parliamentary reports connected with friendly . London: Harrison and Co. (printed by), 1842. VIII, 9-47, [1=blank) pp. Second edition. Slim 8vo, Publisher's hard grain cloth, blind-stamped decorative border on covers, slightly cockled and soiled, sympathetically rebacked. Margins lightly browned throughout; Second edition, first published in 1836, of an early actuarial bibliography, limited to one hundred copies (Goldsmiths). 'Since the first appearance of these pages the contents have been increased to more than double the original quantity, as well from the continued researches of the editor; as from the liberal and valuable communications of many of those friends and professional gentlemen to whom he presented copies of the first impression' (preface). Described by DNB as an 'art amateur' for his founding of the Art Union of London, Lewis Pocock (1808-1882) 'was for many years a director of the Argus life-assurance office', as well as 'an extensive collector of Johnsoniana of all descriptions, some time Treasurer of the Graphic Society, an active member of the Society for the Prevention of Cruelty to Animals' (DNB XVI, 5), and patentee of a scheme for electric lighting. PROVENANCE: John Venn's copy, signed and dated (1882) by him on the title, also with an author's presentation inscription on the half-title, possibly to the genealogist William Berry (1774-1851). The logician John Venn (1834-1923) is known for his large collection of books on logic, now housed in the Cambridge University Library (see the Catalogue of a Collection of Books on Logic, Cambridge, 1889), as the writer of The Logic of Chance (1866), Symbolic Logic (1881) and The Principles of Empirical Logic (1889), all of which became 'highly esteemed textbooks in the late nineteenth and early twentieth centuries' (DSB), and as the eponymous inventor of the Venn diagram. 'Venn entered Gonville and Caius College, Cambridge, in 1853; took his degree in mathematics in 1857; and was elected a fellow of his college, holding the fellowship until his death. He took holy orders in 1859, but after a short interval of parochial work he returned to Cambridge as college lecturer in moral sciences and played a considerable part in the development of the newly established moral sciences tripos examination … He received the Cambridge Sc.D. in 1883 and in that year was elected a fellow of the Royal Society' (DSB XIII, 611). Goldsmiths' 32867; Institute of Actuaries, p. 132, the Venn copy, not in Utrecht, RKN 40; Kress C.5921. Rare, not in COPAC, BL and LoC. € 1.875,00

[033681] Napier, John MacDonald, William Rae. THE CONSTRUCTION OT THE WONDERFUL TABLE OF LOGARITHMS. Edinburgh: Blackwood, 1889. translated from Latin into English with Notes and a Catalogue of the Various Editions of Napier's Works by William Rae MacDonald. This volume thus contains a translation of Napiers Constructio and notes and a bibliography by Macdonald. First Edition, XIX, 169, (3) pp. 4to (260*200 mm). Original quartervellum with burgundy cloth boards. Title and dating (1619/1889) on 2 burgundy leather labels in gilt on spine. Uncut heavy paper (watermark J. Whatman), evidently a deluxe edition on better and larger paper than the trade edition. PROVENANCE: Sidney Melmore, his bookplate at fpep.

An excellent bibliography with the most exact collations available. The CONSTRUCTIO (here in 1st English translation) is very clear in how Napier calculated his logarithms.

Tomash N13. € 480,00

[023261] Waller Zeper, C. M.. DE OUDSTE INTRESTTAFELS IN ITALIE, FRANKRIJK EN NEDERLAND MET EEN HERDRUK VAN STEVINS "TAFELEN DER INTEREST". Amsterdam: N.V. Noordhollandsche Uitgeversmaatschappij, 1937. First Edition. (12), 95, (1), 92 pp. Original off-white wrappers with black title on frontwrapper and spine.

Doctoral thesis at Leiden University. The 92 pp. are a reprint of the 1572 Plantin edition of Simon Stevin: Tafelen van Interest. The original Stellingen laid in. With an inscription by a female family member (Judith): "van den schrijver gekregen, 26 maart 1937", which is 10 days before the thesis was defended.

Not in Tomash. € 100,00

[023164] Fletcher, A. , J.C.P. Miller and L. Rosehead. AN INDEX OF MATHEMATICAL TABLES. London: Scientific Computing Services Limited, 1946. First UK Edition. VIII, 450, (2=corrigendum) pp. 248*157 mm. Original burgundy cloth with gilt title and Scientific Computing Service (=UK binding) on spine. Printed in the UK (see verso of title). PROVENANCE: Small library blindstamp of Birkbeck College on ffep and title, small stickers from spine now pasted on loose library slip from the same provenance stamped cancelled.. Some minor edgewear.

As the foreword says: prepared under the difficulties and distractions of war-time conditions. Rosenhead (Professor) comes after his 2 lecturers and co-autors because he was absent on active service during most of the production period. The index encompasses 24 catagories of tables from logarithms to Bessel functions. Includes math tables only, so no annuities for instance. With an emphasis on most recent, however also data on first editions are included. For logarithms only the more important tables are included, as for this subject also Henderson is available. For this reason one does not find Ozanam (1685) and most Wolff-related tables. For other catagories completeness is envisaged. Explanation and evaluation (372 p.) and bibliography (78 p.). The latter only includes author, title, city year, which is adequate however as collation and binding then can be found in other sources. The merit of this book is the comprehensive summary of titles not easily found in libraries and poorly documented by often lacking bibliographies in the tables. Mentions Herwart von Hohenburg, Tabulae Arithmeticae, 1610, which precedes Briggs 1624 by 14 years (however is it a comparable table?). Also an early stereotyped table by Lalande (1818) I did not know of before. A very helpful research tool.

OOC 606. Tomash F78, the US edition. € 300,00

[033601] Fletcher, A. , J.C.P. Miller and L. Rosehead. AN INDEX OF MATHEMATICAL TABLES. New York: McGraw-Hill Book Company, Inc, 1946. First American Edition. VIII, 450, (2=corrigendum) pp. 240*157 mm. Original black cloth with gilt title and McGraw-Hill Book Company on spine (=American binding). Printed in UK (see verso of title). Some minor traces of library as former owner.

As the foreword says: prepared under the difficulties and distractions of war-time conditions. On title Rosenhead (Professor) comes after his 2 lecturers and co-authors because he was absent on active service during most of the production period. The index encompasses 24 catagories of tables from logarithms to Bessel functions. Includes math tables only, so no annuities for instance. With an emphasis on most recent, however also data on first editions are included. For logarithms only the more important tables are included, as for this subject also Henderson is available. For this reason one does not find Ozanam (1685) and most Wolff-related tables. For other catagories completeness is envisaged. Explanation and evaluation (372 p.) and bibliography (78 p.). The latter only includes author, title, city year, which is adequate however as collation and binding then can be found in other sources. The merit of this book is the comprehensive summary of titles not easily found in libraries and poorly documented by often lacking bibliographies in the tables. Mentions Herwart von Hohenburg, Tabulae Arithmeticae, 1610, which precedes Briggs 1624 by 14 years (however is it a comparable table?). Also an early stereotyped table by Lalande (1818) I did not know of before. A very helpful research tool.

OOC 607. Tomash F78. € 300,00

[054016] Campbell-Kelly, Martin and others, Editors. THE HISTORY OF MATHEMATICAL TABLES. Oxford: Oxford University Press, 2003. VIII, [2], 361, [1] pp. Original red cloth with title in white on spine. Pictorial dustjacket printed in red.

12 papers by various authors from Sumer to spreadsheets. € 45,00

[053963] Horsburgh, Ellice Martin. NAPIER TERCENTENARY CELEBRATION. handbook of the exhibition of Napier relics and of books, instruments & devices for facilitating Calculation.. Edinburgh: Royal Society of Edinburgh, 1914. VII, (1), 343, (1), XII pp., [7] leaves of plates. Original grey wrappers printed in black. Spine professionally restored. In black drop-back box with red tetteringpiece on spine. PROVENANCE: Sir Edmund Whitaker, professor of mathematics at the University of Edinburgh and convener of the committee that prepared the Tercentenary Handbook Given to Robert Schlapp by Lady Whitaker in May 1956, see his note on title. Schlapp's handwritten name on inner front wrapper. Letter laid in from Ellison (Royal Observatory) returning the book in 1958 after a loan. FIRST EDITION of the rare catalogue presented to those who attended the exhibition.

It is the best account of the state of mechanical calculation up to World War I. The Napier tercentenary celebration, marking the three hundredth anniversary of the publication of Napier's Mirifici logarithmorum canonis descriptio (1614) was held in Edinburgh from July 24 to July 27, 1914--just preceding the start of World War I on July 28. Participants in the exhibition included individuals and companies from Scotland, England, France, and Germany The meeting was intended to be followed by a colloquium on the mathematics of computation, but that was canceled because of the war conditions. The Handbook was published in two forms: this softcover version, presented to those who registered for the exhibition; and a hardcover version issued for sale under the title Modern Instruments and Methods of Calculation. Relatively few copies of the softcover version seem to have been distributed at the exhibition, partly because the exhibition took place in Edinburgh, but mainly because war broke out just after it began. Randell 1982a, 476. This version is unusually scarce.

OOC 322. Not in Tomash. 1 copy in NCC (Delft), 2 copies in COPAC (Oxford and National Library of Scotland), none in OCLC. € 1.200,00

[053964] Horsburgh, E. M. (editor). MODERN INSTRUMENTS AND METHODS OF CALCULATION. A HANDBOOK OF THE NAPIER TERCENTENARY EXHIBITION. London: G. Bell and Sons, 1915. VII, (1), 343, (5), XII pp, [5] leaves of plates. Original green cloth.

The trade edition of the material handed to those who attended the exhibition. It is the best account of the state of mechanical calculation up to World War I. The Napier tercentenary celebration, marking the three hundredth anniversary of the publication of Napier's Mirifici logarithmorum canonis descriptio (1614) was held in Edinburgh from July 24 to July 27, 1914--just before the start of World War I on July 28.

OOC 323. Tomash H166. 1 copy in NCC (Amsterdam). Over 10 copies in COPAC and OCLC. € 700,00

[053965] Knott, Cargill Gilston. NAPIER TERCENTENARY MEMORIAL VOLUME. London: Longman, Green and Co, 1915. XI, (1), 441, [3] pp. Original cream cloth, gilt-stamped on front cover and spine. Original burgundy endpapers. Uncut. Very fresh copy, of many copies the cloth is a bit dirty and of this copy further the endpapers are mint.

An elegantly printed collection of addresses and essays delivered before the International Congress which met in Edinburgh on 24-27 July, 1914, to commemorate the Tercentenary of the publication of John Napier's 'Mirifici Logarithmorum Canonis Descriptio'. On July 28 Austria-Hungary declared war to Serbia and on August 4 Germany invaded Belgium, thus triggering a UK declaration of war.

OOC 331. 14 copies in COPAC. Tomash K56. € 400,00

[023187] Henderson, James. Bibliotheca tabularum mathematicarum. Being a descriptive catalogue of mathematical tables. Bd.1: Logarithmic tables. . London: Cambridge University Press, 1926. First Edition. IV, 208 pp. With a facsimile of the title and preface of TWEEDE DEEL DER NIEVWE TEL-KONST (1627) on 2 leaves between the Roman and the arabic numbered pages. Original blue-gray wrappers printed in black. Handwritten title on spine. With a foreword by Karl Pearson.

A rare copy of the most important biliography of mathematical tables, with an emphasis on Briggsian logarithms (126 p.). As far as I know this is the only edition ever published.

Tomash H 99. 5 copies in COPAC. € 450,00

[023493] Wijngaarden, A. van, A. B. Frielink, H. van der Weg, E. W. Dijkstra. NRMG 1959-1964. Amsterdam: Nederlands Rekenmachine- genootschap, 1964. First Edition. 71, (1) pp. Original white wrappers printed in red. A colofon states, that the text was written on various flexowriters and processed for proper cut-off of sentences (aligning left and right) on the good old Electrologica X1, then at the Mathematisch Centrum. The program was written by Hugo Brandt Corstius. This same module is said to be still to be operating in Microsoft Word. Thus this booklet is THE VERY FIRST TEXT ALIGNED BY A COMPUTER. The texts of presentations, in which Van Wijngaarden (died in 1987) presents a copy of Den Decker (Tweede deel...) and 2 Vlacq (1628) tables borrowed from the libraries of Utrecht and Hollandsche Societeit.

Not in Tomash, no other copy anywhere. € 100,00