
MATHEMATICS
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]
A Concise Overview for a
Very Special Student Subset
(“Abregé”). Le Blond, Guillaume. Abregé de geometrie à l'usage des pages de la Grande Ecurie du Roy. Où l'on donne ce qui est le plus nécessaire pour entrer dans l'étude des fortifications. Paris: Joseph Bullot & Jombert, 1737. 12mo (16.9 cm, 6.7"). [4], 162, [6] pp.; 5 fold. plts.
$450.00
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First edition of this introduction to geometry, intended for
young men working in the royal stables who had only scant time available for the study of mathematics. In addition to a mathematician, professor, and contributor to Diderot's Encyclopédie, the author (1704–81) was a scholar of military tactics, responsible for Éléments de tactique and Traité de l'attaque des places among other items.
This now-uncommon textbook is illustrated with five folding engraved plates of diagrams. WorldCat shows
just one U.S. institution (Society of the Cincinnati) reporting a copy, and only a handful of overseas holdings.
Provenance: Title-page with early inked inscription “de Ratzenried” and front pastedown with von Ratzenried armorial bookplate (coat of arms showing greyhounds and a moon with clouds) labelled F.C.V.R.: possibly Franz Carl Anton von und zu Ratzenried.
Contemporary mottled calf, board edges with gilt roll, spine with raised bands, gilt-stamped leather title-label, and compartments gilt extra; light wear overall, edges and joints moderately rubbed. All edges speckled red. Bookplate and inscription as above. Pages with occasional small pencilled marks of emphasis, otherwise clean; one plate with outer edge slightly tattered.
A very nice copy, in contemporary binding, of a scarce practical compendium. (40246)
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First Edition of a CLASSIC Building Shapes EFFICIENTLY
Alberti, Giuseppe Antonio. Trattato della misura delle fabbriche nel quale oltre la misura di tutte le superficie comuni si da ancora la misura di tutte le specie di Volte, e d'ogni specie di solido, che possa occorrere nella misura di esse. Venezia: appresso Giambattista Recurti, 1757. 8vo (21.4 cm; 8.5"). Engr. frontis. port., xxxii, 279, [3] pp., XXXVIII plts.
[SOLD]
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First edition of an important work on stereometry — meaning the volume measurement of solid figures — as it relates to architecture, from an influential Bolognese architect and mathematical writer who also invented his own land surveying tools.
The text has been expertly set to include both complicated and extended formulas and is complete with
37 full-page plates and one folding engraved plate depicting the various measurements and angles to be taken into consideration when building with various shapes. Alberti uses the research of other architects and theoreticians — including Jousse, Blondel, Sangallo, Parent, La Hire, and Varignon — in the explanations of various mathematical problems.
Binding: Original cartonné binding; title inked on spine, text untrimmed and partially unopened.
Catalogo ragionato dei libri d’arte e d’antichità posseduti dal conte Cicognara, 389; Riccardi, P. Biblioteca matematica italiana, vol. I, col. 16–7. Bound as above, gently rubbed with squiggle of wormtracking through front board and first leaves including half title/frontispiece, portrait, and title-page, with delicate repairs thereto. Two central sections with light staining to upper outer corners, as of old, very light blue ink; some late leaves with slim crescent of old and likewise light waterstain just into top margins; two leaves with limited in-press ink smears (and a few mispaginations). Nice copy of an important work. (37209)
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Studying DESCARTES' Principles
Descartes, René; Florimond de Beaune; Johan de Witt; & Frans van Schooten; Rasmus Bartholin, ed. Renati des Cartes Principia matheseos universalis, seu introductio ad geometriae methodum. Francofurti ad Moenum: Sumptibus Friderici Knochii, 1695. 4to (21.3 cm, 8.3"). [8], 420, [4], 423–68, [2] pp.; diagrs.
$1250.00
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Important gathering of Cartesian mathematical thought, opening with van Schooten's Latin introduction to and commentary on Descartes' La Géométrie, followed by De aequationum natura, constitutione, & limitibus by de Beaune, Elementa curvarum linearum by de Witt, Tractatus de concinnandis demonstrationibus geometricis ex calculo algebraïco by van Schooten, and the closing Notae et animadversiones tumultuariae in universum opus by Bartholin, who edited the texts. Each work has a separate title-page, and numerous equations and small in-text diagrams appearing throughout; the volume ends with a one page list of errata, chiefly of errors in the mathematical notations.
The trio here was first published as the second volume of the two volume edition of the Latin translation of Descartes' Geométrie, issued in Amsterdam by the Elzevirs, 1659–61.
Provenance: From the residue of the stock of the F. Thomas Heller bookselling firm (est. ca. 1928).
Searches of NUC and WorldCat locate only four U.S. libraries (UChicago, U.S. Naval Observatory, UMinnesota, Linda Hall) reporting ownership.
VD17 3:301520H. 19th-century half calf and marbled paper–covered sides, spine with gilt-stamped leather title and date label; mildly rubbed overall. Title-page with rectangular portion on either side of printer's device excised and repaired (repair apparently done some time ago), with excision just barely touching the ends of the motto banner. First few leaves browned; foxing and offsetting throughout.
A worthwhile exploration of mathematical thought as it stood toward the close of the 17th century, and a good solid copy. (39902)
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The Usefulness of
New SCIENCE & Its Instruments
Glanvill, Joseph. Plus ultra: Or, the progress and advancement of knowledge since the days of Aristotle. London: Pr. for James Collins, 1668. Sm. 8vo (17.8 cm, 7"). 36, 149, [5] pp. (1 final adv. f. lacking).
$1500.00
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First edition: “An account of some of the most remarkable late improvements of practical, useful learning: to encourage philosophical endeavours. Occasioned by a conference with one of the notional way.”
Glanvill defends the advances of science and the Royal Society's scientific method in this rather pugnacious response to controversy caused by an “enrag'd Antagonist” (the Puritan theologian Robert Crosse) who “reported [the author] an Enemy to the Scriptures” (p. 141) and charged him with atheism. Here, Glanvill describes recent progress in chemistry, anatomy, algebra, geometry, astronomy, geography, and natural history, along with advances in instruments such as the telescope, microscope, thermometer, and barometer.
ESTC R14223; Wing (rev. ed.) G820. Recent marbled paper–covered boards, spine with gilt-stamped leather label, lacking final advertisement leaf (only); imprimatur leaf mounted, small repairs to upper margins of title-page and first few leaves. Pages browned and cockled, two with a few letters partially obscured from apparent adhesion one to the other some time ago; text overall very readable. A few instances of annotations, mostly biographical, in an early inked hand.
Despite internal wear, now solid for use and attractive on shelf. (41357)

A Game with Forfeits, a Dictator, & Mirth
(Illustrated Rhyming Game). The gaping, wide-mouthed, waddling frog: A new and entertaining game of questions and commands with proper directions for playing the game and crying forfeits: Embellished with thirteen coloured engravings. [London]: Republished by Field & Tuer, 1887. Small 8vo (18.5 cm, 7.25"). [4], iv, [7]-29, [2] pp., [4 (ads)] ff.; [1] plt., col. illus.
$145.00
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Riddles and COUNTING-OUT rhymes, all part of a fun game whose instructions serve as a preface. The text is printed on one side of a leaf only and
each printed page has a hand-colored illustration.
The work was first printed by Dean & Munday in 1823 and is here presented as vol. II in the Leadenhall Press “Series of Forgotten Picture Books for Children.”
Provenance: From the children's book collection of Albert A. Howard, small booklabel (“AHA”) at rear.
Buff-color printed wrappers with hand-colored vignette on front wrapper; stitched, head and foot of spine chipped, rear wrapper detached and reattached with archival tissue. A good++ copy. (38873)
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Learning the Times Tables with Hand-Colored Pilgrims,
Cherries, Dogs, & Brandy Balls
(Juvenile Mathematics). Grandmamma Easy's merry multiplication. [London]: Dean & Co., [ca. 1850]. 8vo (25 cm, 9.84"). 8 ff.; col. illus.
[SOLD]
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Children's multiplication guide, engagingly presented as an illustrated poem rather than plain old boring mathematical tables. Each leaf is printed on one side, and the
title-page vignette and 16 wood-engraved illustrations have been hand-colored. This item comes from the publisher's “Grandmamma Easy's Pictorial Books” series, and is now uncommon: a search of WorldCat finds only four U.S. institutions reporting holdings of this first edition: There seem to have been one later printing and definitely several subsequent American printings.
The back cover lists the titles of six series' worth of Dean & Son's “original and superior coloured six-penny books” for children.
Provenance: Front cover with early inked ownership inscription of Spencer William Wiles, 1855[?, date partially rubbed]; most recently in the chidren's book collection of American collector Albert A. Howard, small booklabel (“AHA”) at rear.
Osborne Collection, p. 711 (giving speculative date). Publisher's half cloth and printed paper–covered sides; lightly rubbed and dust-soiled, inscription as above, endpapers skillfully refreshed. Page corners and edges showing wear, with one outer corner unobtrusively repaired. Overall a solid copy in original binding, interior completely free of any sign of childish handling and
bright, bright, bright. (40807)
Standard & Ground (or Wave?)-Breaking
Medina, Pedro de. Arte del navigare. Venetia: Appresso Tomaso Baglioni, 1609. 4to (20.5 cm, 8"). A4 b4 2A8 B–Q8 R10; [7], [1 (blank)], 137, [1 (blank)] ff.; illus.
$8000.00
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Pedro de Medina’s (1493–1567) Arte de navegar (originally published in Spanish in 1545) was a ground-breaking work on compass navigation, and became a standard manual translated into many languages. Medina was famous as a mathematician and cosmographer, and the king of Spain placed him in charge of examining pilots and masters for the West Indies. This second Italian edition (the first was printed in 1554) was translated by Vincenzo Palentino; it has a title-page in red and black with a woodcut printer’s device, and woodcut initials, tables, and illustrations, many showing how to make celestial observations.
Also included is a woodcut map showing Europe, the Atlantic, and the New World.
Palau 159680; Alden & Landis, European Americana, 609/77; Medina, BHA, 123. Old vellum; red leather, gilt-lettered spine label; some staining, and chipping to edges and label. Old, careful repairs to interior worming occasionally cost individual letters (but never sense) or a little loss to an illustration. Old rubber-stamps and red and black ownership label on title-page; inked notations on title-page and front pastedown. All edges speckled red. (8555)
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Attractively Printed for a Private Individual
An Unrecorded Broadside
Moreno, Jose Manuel. Broadside, begins: Tabla de las fiestas movibles. Puebla: Impressa en la Imprenta de Christoval de Ortega, 1761. Folio (38.5 cm, 15.25"). [1] p.
[SOLD]
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Bachiller Moreno, a citizen of Veracruz, compiled this chart of the moveable feasts of the Catholic Church for the years 1761 through 1816 and had it printed in Puebla, with a very handsome ornamental border, by the son of the founders of the Ortega printing dynasty.
It represents a very uncommon type of job printing, done as it was for a private individual rather than a guild or government entity.The best account of the Ortega family and its typographic history is in Marina Garone Gavier's work cited below.
Unrecorded in the bibliographic record: Not in NUC, WorldCat, CCILA, Medina, Gavito, etc.
Not in Medina, Puebla; not in Gavito, Adiciones a la Imprenta en la Puebla. Marina Garone Gavier, Historia de la imprenta y tipografia colonial en Puebla de los Angeles (1642–1821), pp. 306–73. Removed from a bound volume. A tear into the text repaired from the rear without loss. Very good. (41013)
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Keeping the Theoretical & the Practical in Balance
Ozanam, Jacques. La geometrie pratique, contenant la trigonométrie théorique & pratique, la longimétrie, la planimétrie, & la stéréometrie. Avec un petit traité de l'arithmetique par géometrie. Paris: Charles-Antoine Jombert, 1736. 16mo (16.2 cm, 6.375"). [8], 308, [20 (index)] pp.; 8 fold. plts.
$300.00
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Corrected and enlarged edition, following the first of 1684. Ozanam (1640–1718) was a largely self-taught mathematician who became a teacher and a member of the Académie des Sciences. He published a number of well-regarded treatises on mathematics, including the much-reprinted Dictionnaire mathématique — the first work of its kind in French — and the groundbreaking Récréations mathématiques et physiques. The present work on practical geometry is
illustrated with eight tipped-in folding engraved plates, while its accompanying “petit traité” features numerous in-text diagrams.
Contemporary mottled roan, spine gilt extra with raised bands and gilt-stamped leather title-label; acid-pitted and worn, especially at joints and extremities. All edges stained red. One plate creased near fold with outer edge slightly proud. Pages and plates clean. (40302)
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The First Australian Star Catalogue — “Devoted to the
Heretofore Unknown Parts of the Heavens”
(PRESENTATION COPY)
Rumker, Charles. Preliminary catalogue of fixed stars intended for a prospectus of a catalogue of the stars of the Southern Hemisphere included within the Tropic of Capricorn now reducing from the observations made in the observatory at Paramatta. Hamburgh: Printed for Perthes & Besser, 1832. 4to (25 cm; 10"). 20, xxv pp.
$20,000.00
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One has to say it plainly: this is
a foundation work of Australian science and an important one for the history of world astronomy — the first Australian star catalogue. Christian Carl Ludwig Rümker (a.k.a. Charles Rumker, 1788–1862) was born at Stargard, Mecklenburg-Strelitz, Germany; he studied to be a builder and passed his master builder examination in 1807 but abandoned that career for teaching mathematics. Two years later, he gave that up in favor of the sea and England, serving variously as a midshipman in the East India Company, a helmsman in the merchant navy, a teacher of sea cadets, and an officer on H.M.S.'s Benbow, Montagu, and Albion. His introduction to astronomy came while on Mediterranean service, where he made the acquaintance of Baron Franz-Xaver de Zach, an Austrian astronomer.
He published various papers and his work attracted favorable review. Captain Peter Heywood, under whom he had served in the Montagu, recommended him to Sir Thomas Brisbane, the newly appointed governor of Australia, and Rümker was engaged as the governor's private astronomer; he landed in Australia as a member of the Brisbane party. Once Gov. Brisbane's Parramatta observatory was completed in 1822 he began his work, and made significant discoveries, but friction with Brisbane caused him to resign; he returned to Parramatta in 1826, was appointed the official government astronomer in 1827, and continued thus through the end of the decade.
For his later life, quarrels, and achievements we recommend the fine article in the online Australian Dictionary of Biography.
Rumker’s catalogue of stars visible in the southern hemisphere had both a purely scientific aim and a practical one. The systematic study and cataloguing of the stars visible with the aid of observatory-based telescopy in the southern hemisphere was in its infancy in the 1820s: The Royal Observatory at the Cape of Good Hope was established in 1820 and was the first permanent astronomical observatory in the southern hemisphere. Thus one can see the importance of Parramatta being up and working in 1822. On the practical side, Gov. Brisbane was a naval officer who knew the importance of the stars in navigation. Rumker’s work and his catalogue served both science and the Royal Navy, as he offered “Constants of Aberration and Nutation”; a “Comparison of my Observations with those made by La Caille”; and notes on “Double Stars,” “Magnitudes and Colour of the Stars, Nebula's, &c.,” and so forth — with the grand quotation of our caption being taken from his Preface.
Searches of NUC and WorldCat locate only nine copies in U.S. libraries.
Provenance: Presented to Alexander Dallas Bache, a great-grandson of Benjamin Franklin and at the time of publication of this work a professor of natural philosophy and chemistry at the University of Pennsylvania: “Professor A.D. Bache / with the author's Compts.” in ink on the front wrapper.
Publisher's blue-green wrappers, covers stained and separating; text block stitched as issued. Overall age-toning; occasional foxing; faint waterstaining in upper third of most pages. Overall a good++ copy. (35203)
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Scarce Medical Dissertation — Presentation Inscription from the Doctor
Santy, L. Gervais. Dissertation sur l'application des sciences physiques et mathématiques, aux sciences médicales en général; suivie de l'exposition succincte de la Constitution météorologique et médicale de printemps de 1807, avec une courte description des maladies qui se sont présentées, pendant ce trimestre, à l'Hôtel-Dieu Saint-Eloi de Montpellier. Montpellier: Bonnariq, F. Avignon & Migueyron, 1808. 4to (23.3 cm, 9.2"). 55, [1] pp.
$200.00
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Sole edition of this doctoral thesis on the potential uses of physics and
mathematics in various aspects of medicine including calculating probable outcomes, pathology, hygiene, anatomy, etc., submitted to the Montpellier medical school on 13 February 1808 by a physician born in Pézenas, France. Santy, who dedicated his dissertation to his parents, his uncle, and one of his former mathematics teachers, defended his work before a group of professors including Charles Louis Dumas, the head of the school. Searches of WorldCat find
no U.S. institutional holdings, and only five overseas institutions reporting copies.
Provenance: Title-page with signed inked inscription noting presentation by the author to a Monsieur Robieux as a mark “d'estime, de considération, et d'amitié.” Later from the residue of the stock of the F. Thomas Heller bookselling firm (est. ca. 1928).
Stitched in contemporary paper wrappers, faded to rose-pink and worn. Two spots of pinhole worming throughout, touching letters without affecting sense.
A solid and very readable copy of this uncommon item. (40214)
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Advances in Newtonian Calculus
Simpson, Thomas. The doctrine and application of fluxions. Containing (besides what is common on the subject) a number of new improvements in the theory. And the solution of a variety of new, and very interesting, problems in different branches of the mathematicks. London: John Nourse, 1776. 8vo (21.6 cm, 8.5"). xi, [1], 274, [2], 275–576 pp.; diagrams.
$1200.00
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Simpson (1710–1761) was the self-educated son of a weaver and originally made a name for himself as an astrologer/fortune-teller, dubbed “the oracle of Nuneaton.” After moving to London and becoming a professor of mathematics, he published his New Treatise Of Fluxions in 1737, and followed that in 1750 with The Doctrine and Application of Fluxions — a “vastly more full and comprehensive” textbook in which the principle matters “also to be met with in [the first] Treatise, are handled in a different Manner” (p. v); the DNB describes the latter work as “one of the best treatises on fluxions written in the eighteenth century.” This more mature, thorough treatment of the subject did not appear again until the present 1776 Nourse printing: the stated second edition, “revised and carefully corrected.” The chapters are illustrated with numerous in-text diagrams, and the second part has a separate title-page.
Provenance: From the residue of the stock of the F. Thomas Heller bookselling firm (est. ca. 1928).
ESTC T77585. On Simpson, see: Oxford Dictionary of National Biography (online). Period-style quarter speckled calf with marbled paper–covered sides, spine with gilt-stamped title and gilt-ruled raised bands. One leaf of advertising reported after the second title-page of some copies not present here (with no sign of loss or excision). First few leaves with upper outer corners worn; one tiny spot of pinhole worming to outer margins of first half of volume; a very few ink droplets and small spots of foxing, pages otherwise clean.
An important mathematical treatise, now uncommon on the market, here in a simple but elegant, distinguished, and solid binding. (39974)
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