Category: Mathematics

BUDÉ, Guillaume

BUDÉ, Guillaume. Libri V. de asse, et partibibus eius.

 Venice, In aedibus Aldi, et Andreae Asulani soceri, 1522.

£5000

4to, ff. (xii) 263 (i), aa8 2b4 a-t8 u6 A-N8. Italic letter, some Greek, a little Roman. Aldine device on title and final leaf, light dampstain to lower fore-corner of d1 onwards but generally clean, nineteenth century vellum, spine gilt-tooled with gilt black morocco lettering label. Very occasional light soiling and thumb marks. An impressively clean, crisp and wide-margined copy; a beautiful sample of what an Aldine edition is, printed on excellent thick, fresh and immaculate paper.

First and only Aldine edition of this work concerning Roman coinage, weights, and measures written by the French humanist Guillaume Budé. This is the third edition, which was revised and emended by the author (first edition printed in Paris in 1514; second in 1516). De Asse contributed to the popularity of “Budaues”, as he stylised his Latin name according to the humanist fashion of the time. This essay on measures included also a plea for humanistic studies to accompany study of the Bible and theology. Similar pleas were being made by many other contemporary authors, Erasmus and Thomas More just to mention two among the most important. Jean Grolier (1479-1565) a noted bibliophile, obtained a copy of the book and sent it to Francesco Asula, an associate of the famous printer Aldus with a letter detailing how it wanted it to be printed and published. 

Provenance: George Fortescue, of Boconnoc and Dropmore (1791-1877), blindstamped arms (and ink shelfmark “102 V”) on upper cover.

Adams B3101; Ahmanson-Murphy 212; Renouard 94:3.

EUCLID

EUCLID. The Elements of Euclid; With Select Theorems out of Archimedes…

London, Printed for W. Innys, T. Longman and T. Shewell…, and M. Senex…, 1747.

£300

8vo, pp. xiv (ii) 240 (iv) 68, A-U8 Z 4. Lacking frontispiece portrait. Title-page vignette of putti playing a trumpet and using a compass and a ruler while reading Euclid’s Elements, motto “hinc omnia”; 5 folding engraved plates of many figures. Archimedes’ Theorems have a separate dated title page and pagination, but the Register is continuous. Engraved vignette of a cone, cylinder and a sphere with motto “Una tribus Ratio est”. Large Cheshunt College Library bookplate on front fly with ink shelf mark and label of the Newport-Pagnel Evangelical Institution, book presented by “an anonymous friend”, on upper pastedown. In contemporary gilt-ruled calf, title on red morocco label to spine. Front joint to cover cracked but holding.

William Whiston (1667-1752) was an Anglican priest and mathematician who in 1703 succeeded Isaac Newton as Lucasian professor and, in the following year, he abridged and published the Elements of Euclid for the use of students at Cambridge. Whiston re-elaborated the work on Euclid of the Belgian Jesuit mathematician André Tacquet (1612-60), who wrote many good elementary texts designed as mathematics textbooks for Jesuit colleges. His Elementa geometriae (1654) was his most popular teaching work. This book was essentially constructed from Euclid’s Elements with material from Archimedes. It was a significant piece of work because of the clarity Tacquet demonstrated in presenting the material. Many editions of Elementa geometriae were produced over the next 100 years. For example, the present work appeared in a third edition published in London in 1727. Palladino writes about Tacquet’s Classes of measures: “The classical definitions of ratio and proportion, defined respectively by the third and the fifth definitions of Book V of Euclid’s Elements, were subjected to a rigorous examination in the seventeenth century: among the critics and revisers of those definitions [was] André Tacquet (whose definition of ‘equal reasons’ has inspired generations of mathematicians). … Tacquet devised refined procedures to figure out the ‘equality of reasons’ by approximation.” F. Palladino, On the theory of proportions in the seventeenth century. Two noteworthy contributions: ‘Cuts of rational numbers’ by the Galilean G. A. Borelli and ’Classes of measures’ by the Jesuit A. Tacquet (Italian), Nuncius Ann. Storia Sci. 6 (2) (1991), 33-81.

EUCLID (CLAVIUS, Christoph, Ed.)

Elementorum Libri XV. Accessit XVI. De Solidorum Regularium comparatione. … 

Rome, Apud Vincentium Accoltum, 1574.

£1,350

8vo, two volumes, of which only the second one is here available. The title is nearly identical to the first one, reading “Posteriores” libri sex a x ad xv. Accessit xvi, de Solidorum Regularium comparatione…, ff. 300, A-2O8 2P4. Roman and Italic letter, very little Greek. Title within woodcut architectural frame topped by the emblem of the Society of Jesus, text enclosed in plain rule border, large woodcut printer’s device on verso of final leaf. Decorated woodcut initials and tailpieces. Several diagrams in text. Early marginalia on top of t-p. Upper corner of last three leaves skilfully repaired, no affecting the text. Occasional light spotting throughout. Ink title inscribed by early hand on foot fore-edge. In modern blind-ruled calf over boards, spine in compartments with red morocco label and gilt lettering. An excellent copy, fresh and crisp withal.

This is the second volume only of this 1574 edition of Euclid’s Elementa edited by Christoph Clavius (1537-1612), the Bamberg Jesuit and professor of mathematics at the Collegium Romanum, who supplemented it with his monumental commentary. This Roman publication represents one of the greatest achievements in the history of Renaissance mathematics. “His contemporaries called Clavius ‘the Euclid of the 16th century’. The ‘Elements’, which is not a translation, contains a vast quantity of notes collected from previous commentators and editors, as well as some good criticisms and elucidations of his own” (DSB iii, p. 311).

Adams E-985; de Backer/Somm. II, 1213; Duarte 42; Hoffmann II, 44; STC Italian 238; Steck, pp. 77-78; Thomas-Stanford 19.