BRIGGS, Henry

THE FIRST COMPLETE SET OF TRIGONOMETRICAL TABLES

Trigonometria Britannica: sive De doctrina triangvlorvm libri dvo.

Gouda, Pieter Rammazeyn, 1633.

£5,750

FIRST EDITION. Folio, pp. [viii] 110, [cclxxiv]. *4 A-N4, O3, a-y6, z4, (lacking O4 blank), leaf with corrections inserted after F2. Roman & italic letter, geometric device on t.-p., numerous geometrical diags., woodcut initials & grotesque headpieces, 272 pp. of tables, contemp. autograph ‘Lord Arundell’ at head of t-p with his ms. shelf mark, C18 Arundell bookplate on pastedown, two stamps of the British Astronomical Association in margin of t-p. Light age yellowing, small ink stain to very outer blank margin of four ll. A very good, clean, well margined copy in contemporary English calf, sympathetically rebacked c. 1900, covers bordered with single blind and gilt rules, spine with raised bands, gilt ruled in compartments with gilt fleurons, all edges speckled red.

FIRST EDITION of the first complete set of trigonometrical tables, “containing the natural sines, tangents and secants to the one hundredth part of a degree and to 15 places, which have never been superseded by any subsequent calculations”. The work arose out of discussions between Briggs, professor of geometry at Gresham College, and the great Scots mathematician John Napier, the inventor of logarithms, who in 1614 had published his ‘Mirifici Logarithmorum Canonis Descriptio’. Napier agreed to suggestions by Briggs for adapting his invention more readily to the construction of tables, and the result, entailing prodigious labour, was Briggs’s ‘Arithmetica Logarithmica’ (1624) and the present work. It is clear that the scale of logarithms now in use, in which 1 is the logarithm of the ratio 10 to 1; 2 that of 100 to 1, etc., is due to Briggs, and that Napier’s role consisted simply in advising him to commence at 1 and make the logarithms increase, rather than decrease, with the natural numbers. Briggs is certainly the originator of the principle of logarithms having 10 for their base.

On his death in 1630 the ‘Trigonometria’ was still unfinished, but was completed by his friend Henry Gellibrand, professor of astronomy at the same college, who added a preface explaining the application of logarithms to plane and spherical trigonometry. They also proved highly useful in the advance of systematic geography and navigation, and among the pioneers in this field who benefited from Briggs’s friendship and special knowledge were Samuel Purchas, Capt. Luke Fox and Edward Wright.

“He [Briggs] was a man of the first importance in the intellectual history of his age. He published many books on arithmetic, geometry, and trigonometry, as well as tables for navigation. But, significant though Briggs was as a mathematician in his own right, his greatest importance was as a contact and public relations man”. He was at the center of a group that included William Gilbert, Edward Wright, Thomas Blundeville, Aaron Rathborne, Mark Ridley, Robert Hues, Hackluyt, and John Pell amongst many. “Briggs seems to have been the first person to appreciate the significance of Napier’s invention of logarithms …and from his interview with Napier onwards Briggs used all Gresham College’s resources to popularise this discovery… It has recently been claimed that in calculating his logarithms Briggs used results equivalent to the Binomial Expansion, whose discovery is normally attributed to Newton.” “Gellibrand (1597-1637) another friend and protégé of Brigg’s, completed his master’s work on logarithmic trigonometry tables: wrote on navigation; and demonstrated the secular variation of magnetic declination. His work was known to Mersenne. ” C. Hill. Intellectual Origins of the English Revolution.

A very good copy with excellent provenance; Lord Arundell of Wardour (1606- 1694) commanded gallantly for Charles I in the civil war, was employed by Charles II in arranging the negotiations for the secret Treaty of Dover with Louis XIV, was imprisoned for five years in the Tower during the Titus Oates hysteria, appointed Keeper of the Privy Seal under James II and remarkably died in his bed at the age of 88.

Shaaber B 661. Smith, ‘Rara Mathematica’ p. 621. Honeyman 506. Graesse I 540. Brunet I, 1258.

L1000

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ARCHIMEDES


Opera quae extant. Nouis demonstrationibus commentariisque illustrata. Per Dauidem Riualtum a Flurantia Coenomanum.

Paris, Apud Claude Morel, 1615.

£5,950

FIRST EDITION thus. Folio. pp. [xliv] 549 (i.e. 551), [i]. Greek and Roman letter in double column, commentary in smaller Roman, printed Italic side notes, some Hebrew. Title in red and black with Morel’s large woodcut fountain device, large woodcut floriated and historiated initials, head and tailpieces and typographical ornaments, innumerable mathematical and scientific woodcut diagrams illustrating text, some half page, C19 bookplate on fly. Light age yellowing, title slightly dusty, some marginal spotting, occasional minor stain or spot, small tear from fore-margin of first three leaves. A very good copy, in contemporary vellum over boards, yapp edges, remains of ties, covers a little soiled.

First edition of this important and highly influential version of the works of Archimedes edited by David Rivault (1571-1616) sometime tutor in mathematics to Louis XIII, founder of a scientific salon at the Louvre, along the lines of the Italian academies, and friend of Scaliger, Casaubon and a company of the chief scholars of the day. He was hugely well read and had travelled extensively, speaking Latin, Greek, Arabic and Hebrew. His ‘Académie du Louvre’ was a direct precursor to the Académie Francaise. The work contains the Greek text with a Latin translation alongside and has extensive explanatory notes. This edition was the more or less complete basis for the first proper German edition, translated by J.C. Sturm in 1670 and was the edition read and used by such influential figures as Descartes. It contains all Archimedes’ monumental contributions to science: his discovery of the principle of specific gravity and methods for calculating the centres, circle measurements, the quadrature of the parabola and spirals, techniques of analysis, his theoretical work on mechanics and hydrostatics, an approximation of the value of pi, and his treatment of the numeration of large numbers.“The success of the humanist mathematicians in uncovering, clarifying, translating and providing commentaries on the major scientific texts of the ancient authors should not be seen as peripheral to the scientific revolution. The mastery of the Greek and Latin texts was an essential stage in the attempt to ‘surpass the ancients,’ and the extensive publishing of new and better-understood texts by the classical mathematicians played an integral role in the founding of the ‘new sciences’” Martin Kemp, The Science of Art, p. 76.

Archimedes, fl. Syracuse c250 BC, was the greatest mathematician and engineer of antiquity – “together with Newton and Gauss – [he] is generally regarded as one of the greatest mathematicians the world has ever known, and if his influence had not been overshadowed at first by Aristotle, Euclid and Plato, the progress of modern mathematics might have been much faster. As it was, his influence began to take full effect only after the publication of this first printed edition which enabled Descartes, Galileo and Newton in particular to build on what he had begun.” Printing and the Mind of Man 72 on the Basle edn. of 1544.

BM. STC C17 Fr. A 630. PMM. 72. (1st edn.) Brunet I 384. Riccandi I 43:7 “Quantunque questa raccolta non sia completa pure e’ assai rara e ricercata’. Not in Honeyman.

L1429

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KEPLER, Johannes

THE QUINTESSENTIAL ASTRONOMICAL TREATISE OF THE RENAISSANCE

Epitome Astronomiae Copernicanae.

Linz, Planck, 1618. (with)

Epitomes Astronomiae Copernicanae…Liber Quartus.

Linz, Godefrid Tampachi excudebat Planck, 1622. (and)

Epitomes Astronomiae Copernicanae…Libri V. VI. VII.

Frankfurt, Godefrid Tampachi, 1621.

£32,500

8vo. pp. (ii) 419-932 (xvi), 17-418 (xviii). Roman and Italic letter, some Greek, woodcut initials, head- and tail-pieces, astronomical and geometrical diagrams and illustrations throughout, outer leaf of synoptic table missing (trimmed to binding). Mostly marginal worm trail to first gathering without loss, poor quality paper with intermittent foxing and age browning, a good, un-restored well-margined copy bound in original vellum fragment of C15th antiphonal leaf in red, blue, and brown ink. Ex dono of Joannes Moeri to the Jesuit College at [?], 1668 on first title page.

FIRST EDITION of Books 1-3 and 5-7, second edition of Book 4, in its entirety one of Kepler’s most influential works and the first complete manual of astronomy constructed according to new principles, published as an inexpensive octavo textbook for students in question-and-answer format. It contains Kepler’s three laws of planetary motion around the Sun, and argues that heavenly bodies travel in elliptical orbits at varying speeds rather than in fixed circular orbits, thus making the Copernican system “nearly 100 times more accurate” (DSB). The principles exposed here formed the theoretical basis for Newton’s law of universal gravitation nearly a century later: his Principia (1687) was first introduced to the Royal Society as “a mathematical demonstration of the Copernican hypothesis as proposed by Kepler.”

The first three books outline the mechanics of the earth’s motion, which Galileo focused on in his Dialogo (1632). This controversial subject landed the Epitome on the Index of Prohibited Books in 1619. Kepler extended the first two laws by applying his discoveries concerning the orbit of Mars to other planets, the satellites of Jupiter, and to the moon which, he argued, revolves around the earth. Book IV deals with lunar theory and ‘harmonic law,’ or Kepler’s scale of the distance between the planets, which he describes as the origin of the music of the spheres. “Kepler’s harmonic law, which he had discovered just as the Harmonice was going to press” is explored in greater detail (Gingerich, Johannes Kepler II, A). The composition and publication of this volume was interrupted when Kepler’s mother Katharina was accused of witchcraft. Kepler was much involved in her defense, and eventual acquittal, in 1621.

Books V-VII consider the practical geometry and problems that arise from the more theoretical discussions of elliptical and lunar theory in the first half of the book. They also offer a theoretical explanation for the Rudolphine Tables or maps of constellations began by Kepler in his apprenticeship with Tycho Brahe at his observatory outside Prague, and completed after the astronomer’s death when Kepler was appointed in his place as astrological advisor to Emperor Rudolph II. “From 1630 – 1650 the Epitome was the most widely read treatise on theoretical astronomy in Europe” DSB  7 & 8 p. 302. A rare and very influential work by one of the most famous astronomers even to this day, whose work radically altered the course of modern astronomy.

Although the book has been bound in a curious order, it is complete. Book 4 (++8, Aaa-Mmm8) is followed by Books 5-7 including index and errata leaf (+6, 4A- 4S8, 4T2, 4V8), and finally Books 1-3 with a few gatherings reshuffled (B8, *6, A8, C8-Bb8, Cc6). The almanac is at the very end (**-***4).

Caspar Bibliographia Kepleriana 55, 66, 69. Barchas 1147. BL C17 Ger K112 : “Pt. 1 was published by J. Kruger in Augsburg. Pt. 2 (comprising lib .4) and pt. 3 (lb. 5-7) have separate titlepages. Pt. 2 is a reissue of the 1620 printing by Planck, published by G. Tambach in Frankfurt/M. in 1622 with new first gathering printed there, pt. 3 was published by Tambach in Frankfurt/M in 1621, and printed there”. Houzeau and Lancaster 11831. Not in Kenney.

L1233

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REISCH, Gregorius


Margarita Filosofica…Accresciuta di molte belle dottrine da Oratio Fineo matematico regio. Di nouo tradotta in italiano da Gio. Paolo Gallucci…

Venice, Barezzo Barezzi, 1599.

£7,250

FIRST EDITION thus. 4to. pp. [xxiv], 1138, [ii] Last blank. Italic letter, some Roman. Fine engraved title page with architectural border incorporating figures representing arithmetic, music, geometry, astronomy etc., foliated woodcut initials, large grotesque woodcut headpieces, folding table, innumerable woodcut illustrations in text, many full page, including one woodcut volvelle globe held in on verso with small woodcut printer’s device, “Dr. Andrea Raineri” ms. in slightly later hand on fly. Light age yellowing a few leaves browned, tiny worm hole in title and first two ll. another in blank margin of last three, small tear at inner margin of fldg. plate, occasional light marginal soiling. A very good copy, crisp and clean with good margins in contemporary limp vellum, spine cracked and worn, book block loose, lacking ties.

First edition of Gallucci’s translation of Gregorius Reich’s celebrated and beautifully illustrated encyclopedia with additional material in this edition by Gallucci and including the revisions by the mathematician Oronce Fine from 1535, and some of the additions of the 1512 Strasbourg edition, such as Martin Waldseemüller’s treatises on architecture and perspective, and Masha’allah’s composition of the astrolabe. The Margarita philosophica (the Philosophic pearl) is a beautifully illustrated encyclopedia which was widely used as a university textbook in the early sixteenth century, particularly in Germany; it takes the form of a dialogue between master and pupil – the pupil asks elementary questions and the master answers them in depth. It gives us an intriguing insight into the university curriculum and state of learning and scientific knowledge at the start of the C16th and here in a much revised form in the late C16th. Its author, Gregor Reisch (c.1467-1525), a Carthusian monk and a friend of many of the most celebrated Humanists of his era including, Erasmus, Beatus and Rheananus, was prior of the Charterhouse of St John the Baptist near Freiburg-im-Breisgau from 1503 to 1525 and was confessor and counsellor to the Emperor Maximilian I. He was educated at the University of Freiburg where he received the degree of magister in 1489 and also taught there. The Margarita was conceived as a textbook for his students at Freiburg, among whom were many influential figures of the German Renaissance, notably the theologian Johann Eck. Reisch’s text is divided into twelve chapters. The traditional subjects of the trivium (grammar, logic, rhetoric) and quadrivium (arithmetic, music, geometry, astronomy) each have a chapter devoted to them. Four of the five remaining chapters are concerned with natural philosophy and cover such things as the elements, meteorology, alchemy, the plant and animal kingdoms, optics and memory as well as heaven, hell and purgatory. The final chapter concerns moral philosophy. The additions in this edition are added at the end, a further 300 odd pages, each supplementing a chapter of the main work. The usefulness of the book as an educational tool is much enhanced by a detailed index and the liberal use of marvelous woodcut illustrations. There are two issues of this edition, with apparently no priority, one with Barezzi’s imprint, and another with Somascho’s which is more common institutionally. A very good copy of this wonderful and beautifully illustrated educational encyclopedia.

BM STC C16 It. p. 552. (Somascho imprint) Not in Adams. Brunet IV 1201. Cicognara 3321. Sabin 69132 (Somascho imprint).

L1138

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