
MATHEMATICS
We
Strove to
Resist
the Pun “Math Major”?
(A
Math Manuscript). Major, Nathaniel.
Manuscript Signed. Untitled. On paper, in English. Germantown, Penna., 6
October – 23 December 1799. Folio (33.4 cm, 13"), [43] ff.
$1100.00

Neatly and clearly indited in this large-format manuscript are problems and solutions for "Surveying by the Compass," "Multiplication of Algebraical Quantities," "Multiplication of Compound Surds," "Division of Surds," "Surveying by the Quarter Compass," and "Practical Questions."
It is very likely that Major was a teacher of mathematics at the "college" or "college preparatory" level and that this is his lecture book. The size both of the volume and of the handwriting would make it easy to work from, in the classroom—one could glance over from the blackboard, for prompting.
The manuscript provides a fine window on the teaching of algebra and advanced plane geometry in the Philadelphia region at the end of the 18th century.
Stationer's blank book: quarter sheep with marbled paper sides. Binding scuffed and rubbed. Joints open but covers firmly attached. Internally very good.
WHIST
Cavendish. The laws and principles of whist stated and explained and its practice illustrated on an original system by means of hands played completely through. American edition. New York: Charles Scribner's Sons, & London: Thomas de la Rue & Co., 1895. 8vo. Frontis., x, 318 pp.; illus.
$85.00


Early U.S. edition: History, rules, and strategies of whist, printed in red and black and illustrated with numerous diagrams of card setups.
Publisher's cloth, covers framed in blind, front cover and spine with gilt-stamped title; edges and extremities lightly rubbed, spine darkened with gilt dimmed. Front fly-leaf with inked gift inscription dated [18]96. Pages clean, two with lower corners dog-eared. All edges gilt. (13988)
Ultimately,
a
Sad
Story . . .
Colburn, Zerah. A memoir of Zerah Colburn; written by himself. Containing an account of the first discovery of his remarkable powers; his travels in America and residence in Europe; a history of the various plans devised for his patronage; his return to this country, and the causes which led him to his present profession; with his peculiar methods of calculation. Springfield, Mass.: G. & C. Merriam, 1833. 12mo. 204 pp. (lacking frontis.).
$75.00
First edition. Zerah Colburn's prodigious calculating abilities astounded audiences in America and Europe when he was a small child; as an adult, his skills waned, and he died young without having fulfilled the promise of his early days. Although Colburn does his best in this memoir to justify his father's having taken him away from family and native country, putting him on display for money, and denying him the opportunity to acquire more than bits and pieces of an education, regret plainly looms behind every line praising his father's devotion. The author sums up his experience (which, as his European tour struggled to its impoverished conclusion, included attempts to become an actor and to open a school) by saying that "When sometimes he hears people wishing that they had his privilege of seeing the world, to think of the price at which he purchased this privilege, would suggest the idea that they little knew what it was which they desired" (p. 133), and noting that men should never rely on expectations of being supported by others. In addition to the sorry story of Colburn's career, there are many random tidbits of information on Napoleon's progress, the English public school system, a prominent murder case of the time, and other items that caught the author's interest, as well as an appendix containing numerous examples of his youthful mathematical accomplishments and some suggestions as to how Colburn performed his calculations. Error in pagination: p. 204 misnumbered 104. Includes "A few pieces in rhyme" (pp. 192-[204]).
Sabin 14257. Full brown cloth. Much of spine cloth chipped away, including title and shelving labels. Covers worn, detached, and blind-stamped by the Mercantile Library (now-defunct). Cloth peeling at back cover. Title-page and several other pages rubber-stamped. Library charge pocket on rear pastedown. Paper with waterstains and spots of foxing; outer paper edges somewhat unevenly highlighted by hand with ink, thus framing each page of text on three sides. Pages 159/160 with one corner folded over. Without the frontispiece portrait. Fascinating early account of the perils of childhood celebrity. (7639)
Colson, Nathaniel.
The mariner's new calendar. Containing the principles of arithmetic and practical geometry; with the extraction of the square and cube-roots: Also rules for finding the prime, epact, moon's age, time of high-water, with tables for the same.... London: Pr. for Messrs. Mount & Page, 1783. 4to (19.8 cm, 7.75"). 136 pp; illus.
[SOLD]
Single-click
any image, for an enlargement.
A very popular and necessary nautical almanac first published in 1676 and very frequently republished until 1785, Colson’s Mariner’s Calendar gives the basic mathematics needed in navigation, the means for reckoning the tide, and the essentials of celestial navigation. This issue, revised by William Mountaine, is not listed in ESTC, and may be a reissue of a previous year’s edition with a variant title-page (tables are given listing the moon’s age for 1780–88).
Not in ESTC. Recent quarter brown calf over marbled paper; round spine divided into compartments by blind rules, two red leather labels (gilt-lettered and gilt-ruled), and gilt date at base. Edges with chipping, tattering, and some bites out, often repaired (with tissue paper) and sometimes affecting printed borders, individual letters, or marginalia. Some light soiling and waterstaining. Rubber-stamps from a now-defunct library, including to half-title and title-page. Ownership inscriptions on half-title. Inked marginalia.
To
Make a
Sundial
. . .
Leadbetter, Charles.
Mechanick dialling: Or, the new art of shadows.... London: E. Wicksteed, 1737.
8vo (20.3 cm, 8"). xvi, 16 pp., pp. (17)(22), 17193, [1] p.; illus,
12 plts.
[SOLD]
Click the interior images for enlargements.
Charles Leadbetter (fl. 1728) taught astronomy, mathematics, and
navigation, and wrote a number of works on these subjects. This is his text
on the "new art" of making sundials, with detailed step-by-step instructionsfrom
calculating and drawing the dial to constructing and painting it. Careful explanations
cover the various types of dials, as well as how to set one's watch by them.
Of
great interest is the section on constructing a celestial sphere.
This
first edition of Mechanick Dialling is printed with
side- and shouldernotes, numerous tables (including those for the latitudes
of many cities), and woodcut in-text diagrams. Of the 12 engraved plates,
11 are detailed sketches of diverse sundials, the twelfth showing a celestial
sphere. This work went on to see a number of editions in the 18th-century
and was twice revised.
ESTC T133701. On Leadbetter, see: The Dictionary of National
Biography, XXXII, 31415. Deep walnut quarter calf over marbled
paper, old style; round spine with raised bands, accented in gilt and with
gilt device in each compartment; red leather title label, gilt-lettered; edges
of leather rolled in blind. Plt. I, bound between pp. 116 and 117, is chipped
on the outside margin, with partial loss of the numerals on that edge. The
printed portion of the last plate, bound in facing p. 125, has been detached
and closely trimmed, just shaving the printed area, and then mounted on the
remaining blank area of the plate. One page with chip out of the upper outer
corner, just touching page numbers; dustsoiling and occasional spotting. Light
inked marginalia on plt. 4.
A delight for the lover of astronomy,
geometry, or chronography.
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


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.

Saenz
de Escobar, José. Manuscript, “Geometria practica y mecanica
dividida en tres tratados[.] El primero, de medidas de tierras, el segvndo, de
medidas de minas, el tercero, de medidas de agvas...para la instrvccion de alcaldes
mayores, corregidores, receptores, y medidores de tierras de esta Nveva Espana.”
In Spanish, on paper. [Guadalajara?, Mexico City?, 1706]. Folio, 142 ff.
$25,000.00

Experience arguing cases before the supreme courts (audiencias) in Guadalajara
and Mexico City gave Saenz de Escobar great knowledge about how those courts
wanted things done when it came to cases involving boundary disputes and ownership
claims involving land, mines, and water. He brought his accumulated knowledge
together in an extended text written expressly for the education of minor officials
associated with courts of the first instance and for surveyors, and, in the
form of the beautifully produced manuscript in hand, his document is of paramount
importance in several kinds.First, contemporary treatises explaining the bases of Novohispanic
court decisions are rare, leaving researchers to guess, with greater or lesser
sophistication, at the reasoning of the judges in applying the law. Sr. Saenz
de Escobar’s careful explications—“this is how the court
insists that this be done”—permit confident study of long-important
cases involving such notables as the Condes de Regla and de Bibanco, while
also illuminating cases of boundary dispute not bringing such wealthy families
into the arena of the court system.

Secondly,
this work is a treatise, full of data and diagrams, on New World methods of
survey, measuring, and estimating: That is, it is a mathematico-scientific
treatise written by a native of New Spain for professionals working in New
Spain. Such treatises are also extremely rare, the more so if illustrated
as in the case at hand.
Finally,
as “working” documents go, this is a truly handsome one. The manuscript
is written throughout in a fine, clear, near-calligraphic hand; consciously
calligraphic main and sectional title-pages are provided. The science and
mathematics involved in accurate measuring and surveying are not only concisely
explained but illustrated with marvelous diagrams—diagrams much more
elegant and, often, embellished than would be necessary. A few instruments
are also illustrated in detail.
This text was important enough to be circulated, in manuscript,
and it was important enough that other copies have survived; a microfiche,
itself very rare, has been made of one of these. But remarkably it has remained
unpublished—a treatise that will support considerable research, and
enhance other research, by a variety of scholars.
Contemporary sheep, flat spine; spine gilt extra. Binding lightly abraded.
Sprat, Thomas. The history of the Royal-Society of London, for the improving of natural knowledge.... The second edition corrected. London: Pr. for Robert Scot & others, 1702. 4to. (21 cm, 8.25"). [8] ff., 438 pp.; 2 foldout plts.
$675.00

Thomas Sprat (1635–1713) was bishop of Rochester, dean of Westminster, and a leading Tory and High-Churchman. He was also a wit and man of letters with an interest in natural science, and (in addition to being a member himself) was also friends with many of the founding members of the Royal Society, including Christopher Wren and Ralph Bathurst. He was thus well-placed to write the early history of the oldest scientific society in the British Isles and one of the oldest in Europe—therein especially defending the Society against the attacks of those philosophers who questioned the value of experimental science.
First published in 1667, this work is here in the second of numerous editions. It includes accounts by members of their scientific work: The two plates illustrate meteorological instruments and the principles of artillery recoil.
ESTC T131282. On the Royal Society, see: Encyclopædia Britannica, 11th ed., XXIII, 791–93. On Sprat, see: The Dictionary of National Biography, LIII, 419–24. Recent quarter red morocco over marbled paper. Beading on spine bands and gilt quatrefoils in compartments; gilt-lettered title, author, and date. A foliate gilt roll at edge of leather on covers. Leaves sometime exposed to moisture and cockled, with shallow chipping and light to moderate soiling. Perforation-stamp on title-page, and rubber-stamps, including one on title-page, of a now-defunct library. All edges speckled red.
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