Best And Most Complete Edition of Briggs Work on Decimal Logarithms, Complete with the First English Translation
BRIGGS, Henry. Logarithmicall arithmetike. Or Tables of logarithmes for absolute numbers from an unite to 100000; as also for sines, tangentes and secantes for every minute of a quadrant: with a plaine description of their use in arithmetike, geometrie, geographie, astronomie, navigation &c. These numbers were first invented by the most excellent Iohn Neper Baron of Marchiston, and the same were transformed, and the foundation and use of them illustrated with his approbation by Henry Briggs Sir Henry Savile Professor of Geometrie in the Vniversitie of Oxford. The uses whereof were written in Latin by the author himselfe, and since his death published in English by diverse of his friends according to his mind, for the benefit of such as understand not the Latin tongue. London: George Miller , 1631.
[Together with]

[BRIGGS, Henry], [VLACQ, Adrianum]. Arithmetica logarithmica sive Logarithmorum chiliades... Editio secunda aucta per Adrianum Vlacq. Goudae: Excudebat Petrus Rammasenius, 1628.

Best and most complete edition and the first English edition. Our present copy contains the 1628 Gouda "second edition" or rather Vlacque's first edition, and the first English edition of Briggs' introduction. Folio (13 x 8 3/4 inches; 331 x 221 mm). [2], 54, [8, table of latitudes], [2, blank]; [6], 79, [1, blank], [2, table half-title], 764 pp. 1628 edition lacking errata leaf in the preliminaries. Title-page of 1628 edition printed in red and black. Vignette printer's device on 1631 title-page.

Later paneled mottled calf. Boards tooled in blind. Spine stamped in blind, lettered in gilt. Some minor wear to boards. Previous owner's ink notes to pastedowns. Armorial bookplate tipped-in to verso of 1628 title-page. Some staining to leaf Rrr2, otherwise very clean. Overall very good.

First edition in English of Brigg's great work on decimal Logarithms, together with Vlacq's "Second Edition" in Latin along with Vlacq's most complete Logarithmic tables. Even though the title-page states "Editio Secunda" it has been called an entirely new work by the British Library.

Although Briggs took much influence from mathematician John Napier who is generally credited for the discovery of logarithms, "Briggs' Arithmetica logarithmica was the first to publish logarithmic tables based on the decimal system such that log 1=0 and log 10=0; the common logarithmic tables currently in use are derived from those of Briggs..." (Norman 339, regarding Briggs' first edition of 1624.)

After Briggs published his work of 1624 which consisted of 30,000 tables, from 1-20,000 and from 90,000-100,000. In 1628, Adriaen Vlacque published what he called Briggs "Second Edition" even though Vlacque had subsequently filled in the remaining 70,000 tables. Due to all these additional calculations by Vlacque, it has been noted that Vlacque would have been completely warranted to call this an entirely a new work, rather than the second edition. "To return to the original calculation of the logarithms of numbers Briggs, as has been stated, published the logarithms of the numbers from 1 to 20,000 and from 90,000 to 100,000 to fourteen places in his 'Arithmetica.' There was thus left a gap from 20,000 to 90,000 which was filled up by Adrian Vlacq (although Briggs had in the mean time nearly completed the necessary calculations; see Phil Mag. May 1873), who published at Gouda in 1628, a table containing the logarithms of the numbers from unity to 100,000 to 10 places of decimals. Having calculated 70,000 logarithms and copied only 30,000, Vlacq would have been quite entitled to have called his a new work. He designates it, however only a second edition of Briggs..." (Report of the Forty-Third Meeting of the British Association for the Advancement of Science; Held at Bradford in September 1873. Pg. 51)

Of the British library copy, they have Vlacque's Tables along side the English introduction. They call for a variant with the Latin introduction rather than the English. This present copy has both the English as well as the Latin. "The table of logarithms begins an unpaginated section collating A-3R? 3S?. It consists of sheets from the 1628 edition printed in Gouda. A1r is a divisional title, either in Dutch ("Tafel der logarithmi voor de ghetallen van 1 af tot 100000") or Latin (not seen). Within this series, "Canon triangulorum" has divisional title. Variant: with the Latin introduction to the tables from the Gouda edition...Not in fact a translation of "Arithmetica logarithmica", but a different work." (From British Library copy ESTC, S107123)

"This table of Vlacq's was published, with an English explanation prefixed, in London in 1631, under the title Logarithmicall Arithmetike or Tables of Logarithmes for absolute numbers from an unite to 100,000... London, printed by George Miller 1631...Wilson (in his 'History of Navigation,' prefixed to the third edition of Robertson) says that some copies of Vlacq of 1628 were purchased by our booksellers, and published at London with an English explanation, premised dated 1631." [As is this present copy] (Report of the Forty-Third Meeting of the British Association for the Advancement of Science; Held at Bradford in September 1873. Pg. 52)

ESTC S107123. Sotheran 585. Wolf 195. (Mentioned in PMM 116).

HBS # 68039 $8,500