DEL MONTE, Guidobaldo

MATHEMATICS IN SERVICE TO EARLY THEORIES OF PHYSICS

In duos Archimedis aequeponderantium libros paraphrasis.

Pesaro, Girolamo Concordia, 1588.

£7,500

FIRST EDITION. Folio, pp. (4), 202, (2). Roman letter; title and text within ruled border, large historiated initials, several woodcut illustrations and diagrams; minor repair to blanks of title, occasional oil splashes, mainly marginal. A very good, well-margined copy in contemporary limp vellum; remains of ties, shelf mark and title inked on spine by contemporary Gothic hand; slightly stained, small loss at foot of spine; early bookcase number on front endpaper verso; a few contemporary marginalia, amending the text according to the final errata.

A fine copy of the first edition of an influential translation of Archimedes with the commentary by Guidobaldo del Monte (1545 – 1607), Galileo’s friend and early patron. Born to a wealthy family from Urbino, Guidobaldo was a soldier, military engineer, astronomer and mathematician. In addition to writing innovative works of applied geometry and physics, he also dwelt on perspective theory and developed mathematical instruments, such as the proportional and elliptical compass. His Liber mechanicorum (1577) is regarded as the greatest work on statics since the Greeks. It employed the mathematically rigorous proofs of Archimedean models in investigating static and mechanical questions. Equally important was this paraphrase of Archimedes’s On the Equilibrium of Planes, which applied geometry to hydrostatics and demonstrated the law of the lever using pure geometry.

Both these works had a profound and lasting impact on the methodology adopted by 16th-century Italian scientists, most notably Galileo: ‘Guidobaldo was … possibly the greatest single influence on the mechanics of Galileo’ (ODSB). In addition to his patronage, Guidobaldo also supported Galileo’s race for the chair of Mathematics at the University of Padua in 1592. Galileo himself, who was sent a copy of the present work, adopted Guidobaldo’s analysis of the lever.

BM STC It., 37; Adams, U6; Graesse, I, 180; Ricciardi, II, 179.

L2050

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STÖFFLER, Johannes

THE FIRST 16TH CENTURY ASTRONOMY BOOK

Elucidatio Fabricae ususque Astrolabii

Oppenheim, Jacobus Kobel, 1513 (colophon 1512).

£9,500

FIRST EDITION. ff. xii, lxxviii. Roman and Gothic letter. Title within fine woodcut architectural border, putti above, numerous woodcut diagrams, charts and illustrations, some full-page, those on A6v, C4v and D3r with extension slips (single extension slip of D3 loosely inserted), woodcut arms of George Simler to **6 verso, fine white on black woodcut initials in various sizes, charming criblé white on black printer’s device at recto of last, **6 verso with poem by Philipp Melanchthon, occasional early ink marginalia in and English hand, early English manuscript price mark (3s 4d) at head of title page. Light age yellowing, title page a little soiled, minor restorations to lower blank corners of first three and last two leaves, light, mostly marginal, water-staining, the occasional thumb mark or minor stain, fractionally trimmed at outer margin. A good copy in contemporary speckled calf, sympathetically re-backed, spine gilt ruled in compartments with fleurons gilt to centres, morocco label gilt. a.e.r.

First edition of this hugely important and beautifully illustrated work, the first book of original astronomy published in the C16th. The most comprehensive treatise on the astrolable of its time, it was handsomely printed at the first press in Oppenheim. ‘Stoeffler recognized that, in mapping, computation of the distance between two places whose latitude and longitude were known failed to take into account the convergence of the meridians’ (Stillwell). The poem by Melanchthon, who was Stoeffler’s student, is possibly his first appearance in print.

Johann Stoeffler (1452-1531) was a mathematician, astronomer and instrument-maker who was appointed to the chair of mathematics and astronomy at the University of Tuebingen. His Elucidatio fabricae ususque astrolabii was one of the most influential books published on the astrolabe, with editions extending from 1513 into the seventeenth century. He was the teacher of Philipp Melanchthon, Johannes Schöner, and Sebastian Münster and a key member of the generation who considered Regiomontanus the paragon of Renaissance astronomers. Stoeffler adopted a programme of astronomical observation and publication of tables, and promoted the importance of precision instruments and practical accounts of how they worked. “Stoeffler devotes Part one to the construction of the components of an astrolabe, including marking the lines on the latitude plates; setting out the rete (with the star positions in Latin and Arabic); applying the calendar scale, the shadow square and the unequal hours lines to the back; making the rule, alidade, axis and suspension shackle. Stoeffler also discusses an horary quadrant for equal hours, the use of the shadow square in surveying, and the astrological applications of the astrolabe. Such was the currency of his account that ‘Stoeffler’s astrolabe’ came to stand for fixed-latitude astrolabes, as distinct from the universal ones.” J. Bennett and D. Bertoloni Meli, Sphaera Mundi: Astronomy Books in the Whipple Museum 1478-1600.

The second part of the work gives detailed explanations the use of the astrolabe with equally remarkable woodcut illustrations. Stoeffler ends his work with a discussion of perspective and measurement. Jacob Koebel, the printer of this work, was a surveyor and practical mathematician in Oppenheim, near Mainz. He was also a prolific printer and publisher of his own works. After publishing this work by his friend, Johann Stoeffler, in 1513, Koebel went on to produce his own treatise on the astrolabe.

USTC 649878. BM STC Ger. 834.C16th Adams S1886. Houzeau & Lancaster 3256.  Stillwell Science, 892. Wellcome 6099.

L1995

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EUCLID

LATIN EDITION OF EUCLID’S WORKS

Elementorum geometricorum libri XV.

Basle, Iohannem Hervagium, 1546.

£7,500

Folio, pp. (viii) 587 (i). Roman letter in two sizes, commentary in italic, some Greek innumerable woodcut mathematical diagrams in text. Printer’s woodcut device on title and verso of last, fine white on black historiated Holbeinesque initials in various sizes. Blank fore edge of first gathering slightly frayed, that of the title with early repair, light marginal water-staining in last few gatherings, occasional minor dust soiling. Generally a most attractive copy in strictly contemporary London blind-stamped calf, covers triple blind ruled to a panel design, roll-tooled second panel with lozenge-shaped inner border to both covers (Oldham pl. LI: 866), spine neatly repaired, pastedowns taken from an English rubricated manuscript. c.1400 with decorative initials, eps. from Galen’s De Compositione medic., Basle 1530. C16th autograph and manuscript acquisition note of R. Skene or Shene on title.

A very interesting copy of the second edition of Herlinus’ Latin edition of the collected works of Euclid first printed nine years earlier: it is quite differently set up. A reissue of the Elements edited by LeFèvre, Paris, 1516, “with few changes but with the addition of the ‘Phaenomena, Optica’ etc. For the edition of 1537 the Paris edition was collated with ‘a Greek copy’ by Christian Herlin.” Heath, ‘The thirteen books of Euclid’s Elements’. The text is embellished with the commentaries of Theon of Alexandria and Campanus, in the Latin version of Bartholomaeus Zambertus. “I now come to the Basle editions, an important series, all folios printed by Johann Herwagen between 1533 and 1558. He was the first printer to inset Euclid’s diagrams in text. Earlier printers, and some later, placed them in the fore margin.” Stanford.

This copy is complete with the six-page dedication by Melanchthon to the ‘studiosis adolescentibus’ which is often mutilated or missing (see e.g. Thomas-Stanford copy). “From many copies this introduction has been removed by the clerical censor who has added his stamp” Stanford. A typographically handsome (see full-page reproduction by Thomas-Stanford) and textually significant edition of the “compilation of all earlier Greek mathematical knowledge since Pythagoras, organized into a consistent system (…) the common school textbook of geometry for hundreds of years.” (Printing and the Mind of Man 25 on first Latin edition). The last 100 pages comprise the minor works of Euclid such as the Phaenomena Data, Specularia and Perspectiva. A handsome and interesting copy in a charming contemporary London binding.

BM. STC. Ger. p.288 (at least one imperfect). Adams E 975 (1 ditto). Thomas-Stanford 11. (Full page reproduction)

L1822

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EUCLID

THE MOST FAMOUS MATHEMATICAL TEXTBOOK

Opera.

Venice, Joannes Tacuinus de Tridino, 1510.

£29,500

Folio, 240 unnumbered leaves. (10) A-Z8, AA-EE8, FF6, lacking last blank. Theorems in gothic letter, demonstrations in Roman, first two lines of title woodcut with rich gothic decoration, large woodcut device of St. John the Baptist signed BM beneath. First leaf of text printed in red and black with large white on black woodcut border on three sides of putti, mermen, vines vases (taken from the 1504, Legendario delli sancti), printer’s white on black device on verso of last, fine large white on black historiated and floriated initials, outer margins with printed geometrical diagrams on most pages, “nulla virtus sine labore” in contemporary hand in shield on woodcut border, some contemporary marginalia, including a manuscript diagram on B6. Lower outer corner of title a little thumbed, small worm trail in upper blank margin of first few leaves, occasional minor marginal water staining, the odd spot or ink splash. A very good copy, crisp and clean, on thick paper, in contemporary limp vellum, remains of ties, title manuscript on spine, vellum a little creased and stained.

A lovely example of a beautiful and important book. “It was a translation into Latin from a Greek text by Bartolomeo Zamberti who claims that he has restored and excluded from the exposition of Theon many things that were ‘subversa et prepostere voluta’ in the version of Campanus. For example, the Pythagorean proposition becomes the 47th of the first book as we know it. Zamberti contributes a long preface on the life of Euclid. The thirteen books of the Elements are followed by the Phaenomena and Specularia.

The volume itself is a first rate example of the Venetian book of the time. There is an elaborate title-page with the printer’s well known cut of John the Baptist at the foot. The first page of the text has a fine border, and the larger initial letters are a charming set depicting children playing. In 1510, some of the same sheets were reissued with a freshly printed last page. Both issues seem to be among the rarest of early Euclids” Thomas-Stanford pp. 5-6. In fact this issue is entirely reset after gathering O.

Zamberti’s was a very significant edition. It was the first publication of a Greek based Latin ‘Elements’ as an integral whole, the Greek text he employed was essentially uncorrupted and it is the first to contain translations of a number of the minor Euclidian works. It may not be as superior to Campani’s recension (the first edition) as Zamberti claims but at least it is free of the errors of the mediaeval copyists.

“Euclid’s Elements of Geometry is the oldest mathematical textbook in the world still in common use today.” Printing and the Mind of Man 25 on first edition. This is a lovely, fresh copy, with wonderfully clear impression of the type and woodcuts of this important work, rare in its original binding.

BM STC It. p.238. Thomas-Stanford 5. Essling 284. Sander 2609.

L1425

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RATHBORNE, Aaron


The Surveyor in foure bookes.

London, W. Stansby for W. Burre, 1616

£12,500

Folio, pp. [xii] 228. Roman letter. Fine, large engraved frontispiece portrait of Rathborne by Simon de Passe, engraved title with allegorical figures of Arithmetica and Geometria surmounted by celestial and terrestrial globes and ‘Artifex’ trampling fools and dunces underfoot, and two vignettes of surveyors in the field with their various instruments by W[illiam] H[ole], further engraved portrait of the dedicatee, a young Charles I as Prince of Wales, by F. Delaram. Elaborate woodcut headpieces to opening of each book, geometric woodcut illustrations to text throughout, including a three-quarter page illustration of a quadrant, woodcut initials. O3 is a cancel, fifth line of verso has “58 4/5”. Light dampstaining to lower margin, slight discolouration to upper edge of a few leaves in initial gathering, occasional light thumbmark, paperflaw to outer edge of R3, generally very good. Contemporary vellum over pasteboard, the spine titled in brown ink in a 17th-century hand. A little spotting to outer edge of upper board. Edward Thorne, contemporary ownership inscription to title (deleted), library of the Earls of Macclesfield, their nineteenth-century armorial bookplate to front pastedown, and armorial blindstamp to title and A3.

FIRST EDITION. A very good copy of “the first comprehensive English textbook on Survey” (Singer, vol. III, p. 541). Rathborne addressed the difficulty for contemporary surveyors of computing the areas of fields and estates. He was an advocate of the new decimal arithmetic introduced by Simon Stevin in 1585, and made use of trigonometry, as well as being a staunch supporter of the then relatively new pocket-tables of logarithms. This is one of the most important works of the new kind of vernacular literature on surveying which began to appear at around this time. These offered practical advice for surveyors ‘in the field’, using relatively straightforward equipment, as opposed to concentrating on fanciful advances in scientific instruments. Rathborne presents the basic principles of geometry, and expounds upon their application, as well as discussing instruments useful to the art of surveying (some of them of his own invention, viz. the ‘peractor’ and the decimal chain, an improved version of which is still in use today), and finally discourses on the legal aspects of survey, thus setting out a comprehensive introduction to the practical process of surveying.

The frontispiece portrait of the author here shows him in 1616 (aged 44), in a high ruff, at a desk holding a compass, with other, simple mathematical instruments in the lower spandrels (Hind II, p. 267). The portrait of the dedicatee, the future Charles I as Prince of Wales, by Francis Delaram, shows the future King wearing an elaborate lace collar, and the order of the garter, with his royal arms beneath.

The stunning title-page engraving by William Hole, an English artist active around this time, and mainly known for his portraits and frontispieces, shows “surveyors at work with theodolite and plane-table, their instruments mounted on tripods…readings are entered in an orderly manner in a field-book and plotting is done with a protractor and a mounted needle for pricking points. A bearing-dial or circle termed a ‘circumferentor’ is also in use, and the particular pattern described includes a table of horizontal equivalents on the alidade”. (ibid., p. 542).

STC 20748; Hind II, p. 267; Johnson 27:15; cf. Taylor, Tudor, pp. 154-5.

L384

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POMODORO, Giovanni


La Geometria Prattica

Rome, Andrea Fei for Gio. Angelo Ruffinelli, 1624 [1623]

£4,750

Folio, 58 unnumbered ll., A-M4 N6 O2. Roman letter, captions in Italic. Large engraved architectural t-p, Mars on the right, Victory allegory on the left, pediment with hanging grotesques and putti holding the Savelli arms, repeated on the right and left pedestal, motto ‘agor non obruor’ in between, large Aldine device on verso of last, 51 engraved plates, typographical and woodcut ornaments. Light age-yellowing, fly torn, couple of very sm. ink spots. A very good copy in contemp. limp vellum.

Second edition of this manual for surveyors, architects, geographers, cosmographers, bombardiers, engineers and captains on applied geometry and land surveying, completed by Giovanni Scala at the instance of the brother of Pomodoro after the latter’s death, and first published in Rome in 1599. Afraid of being charged with plagiarism, Scala made clear (cfr. his note at the end of the commentary on pl. VIII) which were his own additions, i.e. all the explanations and captions to Pomodoro’s plates, and seven new plates dealing with the measuring of the volume of parts of buildings such as columns, stairs and spires. Of Pomodoro’s plates, the first represents a selection of measuring instruments such as compasses and square rules; II-XXX explain the rules of the Euclidean geometry concerning triangles etc. (II-XXV), circular figures (XVI-XXIX), and solids (XXX); XXXI-XXXIX deal with the application of these rules to surveying (i.a. the measuring of the area of streets, rivers, moats, lakes, woods, and of the bases of trees and mountains) and XL with the measuring of corners in topography. The last three tackle the measurement of distances (pl. XXXXIII is reproduced in Mortimer). Giovanni Pomodoro was a mathematician of Venetian origin; nothing seems to be know of his life, and this is his only recorded work. Giovanni Scala, a military engineer of Friulan origin, lived in the second half of the C16th. The book is dedicated to Paolo Savelli, named ‘Principe di Albano’ in 1607 by pope Paul III. An interesting treatise made even more appealing by its illustrations, all finely engraved and rich in details and captions.

BM STC It. C17th p. 695. Graesse V p. 399. Riccardi I (2) 301. Honeyman 2513. Mortimer-Harvard It. 394n.

SN2681

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MOLETI, Giuseppe

CELESTIAL COMPUTATIONS FOR THE NEW GREGORIAN CALENDAR

Tabulae Gregorianae Motuum Octavae Sphaerae ac Luminarium. (with) De Corrigendo Ecclesiastico Calendario.

Venice, Petrum Deheuchinum, 1580.

£5,750

FIRST EDITIONS, large 4to., two works in one, ff. (viii) 50, 88 + 37 (i). Roman letter, woodcut initials and ornaments, a couple of astronomical diagrams in text. 88 leaves of astronomical and mathematical tables in first work, within printed line border, 13 of the ecclesiastical and solar calendar in second, the former printed in red and black. Jesuit library stamp and manuscript case mark in blank portion of title page, early manuscript price at head, de-accession label on fly, marginal worm trails to final leaf, well away from text. A splendid copy, with wide margins and very thick paper, crisp and clean in contemporary limp vellum, lacking ties.

Moleti (1531 – 1588) studied at the Jesuit college in Messina, where he was a pupil of mathematics, and published several works on geography and astronomy prior to his appointment as scientific tutor to the young prince of Mantua, Vincenzo Gonzaga. His important Dialogue on Mechanics discusses the problem of the speed of falling bodies of different weights, and anticipates the famous Tower of Pisa experiment of Galileo.

In 1577 he took up the chair of mathematics at Padua, and that year the Roman Congregation appointed by Pope Gregory XIII to reform the Calendar asked his opinion on the topic: his response was the second work comprised here, composed to provide technical arguments in support of the exact correction of the calendar and its astronomical tables, named the ‘Tabulae Gregorianae’ in deference to the Pope. This treatise was then published as an appendix to the astronomical tables of the motions of the fixed stars, the sun and the moon, accompanied by an explanation of the rules of astronomical calculation of the Canons for the Gregorian Tables’ proper use.

Moleti rejected the traditional computation cycles, rebasing the calendar on the real motions of the stars. Moleti’s work did not find favour with his scientific peers, but was much appreciated in Rome (to the tune of 300 Ducats), where the Pope asked him to continue his computations with the motions of the other planets. Moleti’s tables were calculated on the basis of the Copernican system which, as he first realised, Copernicus had based on the exact movements of the heavenly bodies, unlike the earlier Alphonsine tables. This was the earliest practical use by an Italian astronomer of Copernican theory. The resulting Gregorian calendar remains standard to this day. A most attractive copy of an important and very handsome book.

“Questa ediz. va noverata fra le piu splendide del sec. xvi, sia per la bellezza dei caraterri, sia per la qualita della carta e della impressione… Quest’opera redetta per ordine di Gregorio XIII fu quella che procuro all’a maggior fama di distinto astronomo,” Riccardi I 164-65.

Not in BM. STC. IT or Adams.

L1734

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TUNSTALL, Cuthbert

COMMERCIAL MATHEMATICS AND ADVICE FOR BUSINESSPEOPLE OF THE RENAISSANCE

De artes supputandi, libri quator.

Strasbourg, Knoblock per Georg Machaerop, 1544.

£3,950

8vo. pp. (xxiv) 454. Roman and Italic letter, woodcut initials, numerical diagrams throughout. Title page and verso of last slightly dusty, slight damp staining to blank margin of final gathering. Contemporary manuscript ex libris in English italic hand to title page. “T. Liliat’ with Greek inscription, C18 armorial bookplate of William Constable F.R.S – F.A.S. on pastedown. A clean and well margined copy in C17 tan calf, triple-ruled panels in blind with roll-stamped floral motif to one side on covers, richly gilt spine in five ruled compartments with raised bands, C18 paper shelf mark pasted to spine, a handsome copy, all edges red.

The first English book wholly on arithmetic, by the great Catholic humanist, Cuthbert Tunstall (1474 – 1559). The work was Tunstall’s farewell to secular scholarship as he was made Bishop of London a few days after its publication, and thereafter Lord Privy Seal. It is designed as a practical work on arithmetic with the emphasis on commercial transactions, undoubtedly based on models Tunstall encountered during his studies in Padua. “The book includes many business applications of the day, such as partnership, profit and loss and exchange. It also includes the rule of false, the rule of three and numerous applications of these and other rules. It is, however, the work of a scholar and a classicist rather than a businessman.” (Smith p.134, of 1st ed). “He wrote it so that his friends could be empowered to make their own calculations and no longer be cheated by money changers.” (Trapp & Herbrüggen cit infr.).

It is dedicated to his friend Thomas More, who the previous year had been appointed Sub-Treasurer of England, because there was no more appropriate dedicatee than the man engaged in supervising the finances of the King. “The dedicatory epistle to M[ore], gives an interesting picture of M[ore] and Tunstall.” Gibson 157. This was also the return of the compliment which, six years earlier, More had paid Tunstall in the opening lines of the ‘Utopia.’ The work was actually rather too scholarly for ordinary businessmen and it was not reprinted in England. However, it achieved some success on the continent and Rabelais (Oeuvres II 222) mentions it as required reading for the young Gargantua in Paris; it was also prescribed as an arithmetical study text in the Oxford statues of 1549, together with Cardano.

We have not yet been able to trace Thomas Liliat (alternately Layliat/ Lilyat/ Lilliat/ Lelliot), though he was probably a member of the Sussex landowning and later recusant family of that name – hence the obscurity. He must have been a university man, as he knew enough Greek to adapt Aristotle’s quip about Plato’s lack of scientific knowledge, in the original, on the title page. An interesting example of a continental imprint of English authorship returning to England soon after publication, Tunstall having fallen into political incorrectness at home in the interim.

William Constable (1783 – 1806) was an avid naturalist and collector of natural history curiosities. In 1775 he was elected fellow of the Royal Society and his Cabinet of Curiosities is still on display at his family estate, Burton Constable Hall in Yorkshire.

Trapp & Herbrüggen, “The King’s good servant” n. 56. Smith, Rara Arithmetica p. 136.

L1466

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MEURSIUS, Johannes

DE THOU’S COPY

Denarius Pythagoricus.

Leiden, Ioannis Maire, 1631.

£2,750

FIRST EDITION. 4to. pp. 112, (xii). A-O⁴, P⁶. Roman and Greek letter, some Italic. Woodcut printer’s device on title, small floriated woodcut initial, gilt oval book label of George Agar Ellis on pastedown, and of the Wigan free Public Library on fly, their blindstamp to blank margin of title, repeated on last, acquisition note dated 1901 with shelf mark on pastedown. A very good copy in contemporary polished French calf, gilt arms of de Thou and his second wife, Gasparde de la Chastre to covers, spine with raised bands, richly gilt in compartments, with their monogram ‘IAGG’, joints and head of spine a little worn, small repair to tail, all edges red.

Rare first edition of this neo-pythagorian treatise on numbers by the renowned classicist Johannes Meursius in a lovely contemporary armorial binding from the extraordinary collection of Jacques Auguste de Thou. De Thou (1553-1617), scholar and historian, the greatest French book collector of his day, of whom it was long said that a man had not seen Paris who had not seen the library of de Thou. He of course died before 1631, but his son frequently added to his father’s collection and continued to use the final form of his father’s arms on the bindings of his acquisitions.

Johanne Meurius (Van Meurs) was a Dutch classical scholar and antiquary. In 1610 he was appointed professor of Greek and history at Leiden, and in the following year historiographer to the States-General of the Netherlands. As a result of the upheavals caused by the eighty years war he accepted the offer, in 1625, of Christian IV of Denmark to become professor of history and politics at Soro, in Zealand, combined with the office of historiographer royal, in which role he produced a Latin history of Denmark (1630–38), Historia Danica.

This rare and unusual neo-pythagorian work is a short treatise on the significance of numbers. “Photius, in his Bibliotheca, has preserved to us part of a valuable work, written by Nicomachus the Pythagorean, entitled Theological Arithmetic, in which he ascribes particular epithets, and the names of various divinities to numbers, as far as to ten. There is likewise a curious work of the same title, by an anonymous writer, which is extant and only in manuscript. From these two, and from occasional passages respecting numbers according to Pythagoras, found in the Platonic writers, Meursius has composed a book, which he calls Denarius Pythagoricus and which is an invaluable treatise to such as are studious of the ancient philosophy.” Thomas Taylor. ‘The hymns of Orpheus.’

George J Agar-Ellis, First Baron Dover, (1797-1833) was a British politician and man of letters. He was elected a Fellow of both the Society of Antiquaries and the Royal Society in 1816. In 1824 Agar-Ellis was the leading promoter of the grant of £57,000 for the purchase of John Angerstein’s collection of pictures, which formed the foundation of the National Gallery. A very good copy with most distinguished provenance.

Caillet 7488. Not in Thorndike, Brunet, Graesse, or BM STC C17 Dutch.

L1529

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EUCLID

EXTENSIVE EARLY ANNOTATIONS AND DIAGRAMS

Stoicheion Bibl. XV Ek ton Theonos Synousion. Proklou bibl. IV.

Basle, J. Herwagen, 1533.

£37,500

EDITIO PRINCEPS. Folio pp. (vi) 268, 115 (i). Greek letter, title page with printer’s device repeated on verso of final leaf. First leaf of text within woodcut ornamental border (early manuscript Greek index in outer margin), woodcut headpieces and initials, printed mathematical diagrams throughout. Very extensive early Greek manuscript annotations and corrections to the whole of the first 61 pages (Book I) and the last 115 (Proclus’ commentary in Greek and Latin) with numerous manuscript diagrammatic worked examples, very clear and legible. A very good, crisp, clean, widemargined copy, stamp erased from the verso of title page, in polished North European calf, c. 1700.

An important copy of the editio princeps of Euclid’s Elements together with the first edition of Proclus’ commentary. The systematic and close annotations to Book I and the Proclus commentary, where the text has actually been illustrated by way of precise geometric illustrations, make this an extremely valuable copy in determining how both texts were received and used (and the relationship between them) in the first generations after their publication. It is highly unusual to find either of them consistently annotated in the same (or any) hand from beginning to end and even more so where, as here, the annotations constitute a critical commentary and do not just emphasise or note repetition of the text. Book I is the single most important book, in which Euclid outlines all of the fundamental ideas he will expand on in the rest of the work. The volume provides a rare window into the mathematical thought processes of its day. This is the first edition to have printed illustrations incorporated in the text, rather than in the margins, so it is the first in which extensive marginal worked examples were in fact possible.

A work of international, cooperative scholarship, the Greek text was edited by the German Simon Grynaeus, Professor of Greek at Basle, with the assistance of the first Latin translation made directly from the Greek by the Italian Bartolomeo Zamberti, and two Greek manuscripts provided by the Frenchmen Lazare Baif and Jean Ruel. To this Grynaeus added Proclus’ commentary on Book I from a manuscript provided by John Claymond, first President of Corpus Christi, Oxford. The work opens with a long dedication to Cuthbert Tunstall, Bishop of Durham, author of the first printed English arithmetic whom Grynaeus had met through Tunstall’s good friend Thomas More and to whom Grynaeus presented a copy of the present work in thanks for More’s favour during Grynaeus’ visit to England. In fact this was the only comprehensive edition of the Greek text until David Gregory’s in the early 18th century and it formed the basis of all later editions and translations until the 19th century.

“Euclid’s ‘Elements of Geometry’ is the oldest mathematical textbook in the world still in common use today. (…) [It] is a compilations of all earlier Greek mathematical knowledge since Pythagoras, organized into a consistent system so that each theorem follows logically from its predecessor, and in this lies the secret of its success. (…) The ‘Elements’ remained the common school textbook of geometry for hundreds of years and almost one thousand editions and translations have been published.” Printing and the Mind of Man p. 14 on the first Latin edition.

Proclus’ commentary on Book I, here printed for the first time, is of great value in its own right. First, it is a unique source of information on the geometrical knowledge of the thousand years prior to Euclid, otherwise almost certainly lost to us. Second, it is perhaps the earliest significant contribution to the philosophy of mathematics linking it to all sorts of intellectual speculation; Morrow p. xxxii describes it as “one of the most valuable documents in ancient philosophy.” It had not been reprinted up to modern times. The quintessential Renaissance volume and one of the corner stones of modern thought.

BM STC Ger. p. 288. Thomas-Stanford no. 7. Norman 730. Adams E 980. Stillwell II 210. Graesse II “édition encore aujourd’hui indispensable.”

L1541

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