
mathematics  16 titles
Author:
Carl Friedrich Gauss (17771855)
Title/Imprint:
Disquisitiones Arithmeticae
Gerh. Fleischer: Leipzig , 1801
This work, the first textbook on algebraic number theory, is important for its demonstration of the proof of the Fundamental Theorem of Arithmetic, that every composite number can be expressed as a product of prime numbers and that this representation is unique.




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Author:
J. Willard (Josiah Willard) Gibbs (18391903)
Title/Imprint:
Elements of Vector Analysis
Tuttle, Morehouse & Taylor: New Haven , 188184
This is a very rare work printed at New Haven, Connecticut, for use only in Gibbs's classes at Yale (hence the phrase “not published” on the cover sheet). Gibbs, a wellknown scientist in the 19th century, helped develop vector analysis into a useful mathematical tool along with his British counterpart, Oliver Heaviside. Gibbs and Heaviside used the new methods of vector analysis to express Maxwell's laws of thermodynamics in a more concise form (the expressions we now call “Maxwell's Laws”). Our copy of Gibbs's work is particularly interesting since it is his presentation copy to Heaviside and it contains a number of manuscript notes by Heaviside in the text.




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Author:
France. Commision temporaire des poids…
Title/Imprint:
Instruction sur les Mesures Déduites de la Grandeur de la Terre, Uniformes pour Toute la République, et sur les Calculs Relatifs à leur Division Décimale
Saphoux: Macon , 1793 or 1794
This is the first edition of the official manual of the metric system and the first description of the system as it exists today. It was produced the year prior to the compulsory adoption of the system in France. In addition to this copy, the Dibner Library also has versions printed in Paris and Périgueaux.




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Author:
Leonhard Euler (17071783)
Title/Imprint:
Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes
MarcumMichaelem Bousquet & Socios: Lausanne and Geneva , 1744
Euler, a Swiss mathematician who spent most of his life working in St. Petersburg, Russia, was a prolific author and one of the founders of pure mathematics. This work describes his development of the calculus of variations.




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Author:
Gottfried Wilhelm Leibniz (16461716)
Title/Imprint:
Acta Eruditorum
J. Grossium & J.F. Gletitschium: Leipzig , 1684
Leibniz, a German philosopher and mathematician, developed the differential and integral calculus prior to and independently of Isaac Newton. But because neither of them published their findings early on, a contentious debate about priority for the discovery of the calculus raged on for years. Leibniz published this article, on his invention of the differential calculus, in 1684 nine years after he developed it.




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Author:
Apollonius of Perga
Title/Imprint:
Conicorum Libri Quattuor. Una cum Pappi Alexandrini Lemmatibus, et Commentariis Eutocii Ascalonitae
Alexandrus Benatius: Bologna , 1566
Apollonius wrote this great mathematical work in the third century, BC, which is about conic sections, or the planes that result from various ways of slicing through and getting a 2dimensional cross section of a cone. Ellipses, circles, parabolas, and hyperbolas are examples of conic sections. Of the 8 books that made up the Conics, only the first four were known to exist when this book, the first edition of Apollonius, was printed. Books 57 were later discovered in the 17th century. Book 8 has still not been found.




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Author:
François Viète (15401603)
Title/Imprint:
Opera mathematica : in quibus tractatur Canon mathematicus, seu ad triangula…
Franciscum Bouvier: London , 1589
This work is the first part of an uncompleted larger series on geometry. Viete is considered to be the father of modern algebraic notation and this work was critical to the understanding of new ways to solve both plane and spherical triangles. The copy in the Dibner Library is a reissue of the 1579 Paris pages with a new title page from a London printer.




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Author:
John Napier (15501617)
Title/Imprint:
Rabdologiæ, seu Numerationis per Virgulas Libri Duo
A. Hart: Edinburgh , 1617
Napier later extended his use of logarithms in a mecahnical form in this book. He devised a simple method of multiplying and dividing using small rods called "Napier's bones." These rods became the basis for what later became the slide rule (do you remember what that was?)




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Author:
Jakob Bernoulli (16541705)
Title/Imprint:
Ars Conjectandi, Opus Posthumum
[4], 35, [1], 306, [2] p., [3] folded leaves of plates : ill. ; 21 cm. (4to); Impensis Thurnisiorum, Fratrum: Basel , 1713
Jakob Bernoulli was the first in a famous family of Swiss mathematicians. This book, published posthumously, was his greatest work in which he demonstrated the calculus of probability, the theory of combinations and permutations, the thoery of Bernoulli numbers, Bernoulli's law of large numbers, and a discussion of mathematical and moral predictability.


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Author:
N. I. (Nicolai Ivanovich) Lobachevskii (17921856)
Title/Imprint:
Geometrische Untersuchungen zur Theorie der Parallellinien
Mayer & Müller: Berlin , 1887
Lobachevskii developed a new system of geometry that was not dependent on Euclid's parallel postulate. His system of nonEuclidean geometry was first published in an obscure journal in Kazan, Russia. His work was noticed by Gauss, who also developed a similar system independently, and Lobachevskii was finally recognized for his achievements in the 1840s. This original Russian work is extremely difficult to obtain today and our copy is the second edition of the German translation.




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Author:
Janos Bolyai (18021860)
Title/Imprint:
Tentamen Juventutem Studiosam in Elementa Matheseos Purae
2 vols.; Josephum et Simeonem Kali?: Maros Vasarhelyini , 1832
Independently of both Lobachevskii and Gauss, Bolyai produced his own system of nonEuclidean geometry which was published as an appendix to his father's larger work. This privately printed work was poorly printed in a small city in Hungary and few people noticed it at the time. This work is very rare and only four copies of the complete work are known to exist in the world.




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Author:
J. L. (Joseph Louis) La Grange (17361813)
Title/Imprint:
Méchanique analitique
La Veuve Desaint: Paris , 1788
Born in Italy, La Grange spent most of his life in France and was the leading contributor in the fields of number theory and celestial mechanics. Improving on Euler's calculus of variations, in this book La Grange replaced the older synthetical treatments of mechanics with his analytical system.




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Author:
Pierre de Fermat (16011665)
Title/Imprint:
Varia Opera Mathematica
Johannem Pech: Toulouse , 1679
Fermat, along with Descartes, was one of the leading mathematicians of the early 17th century. His pioneering works on the theory of numbers, analytic geometry, and probability are his most notable achievements although he will probably always be remembered for hs famous "Last Theorem" which was not proven until 1995. Fermat's influence during is life was minimal because he published very little. This book, printed after his death, was the first presentation of his significant works and plentiful correspondence.


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