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Cavalieri, Bonaventura

Published by ReInk Books (2017)

Softcover
New

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From: S N Books World (Delhi, India)

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About this Item: ReInk Books, 2017. SoftCover. Condition: New. Reprinted from 1653 edition. NO changes have been made to the original text. This is NOT a retyped or an ocr'd reprint. Illustrations, Index, if any, are included in black and white. Each page is checked manually before printing. As this reprint is from very old book, there could be some missing or flawed pages, but we always try to make the book as complete as possible. Fold-outs, if any, are not part of the book. If the original book was published in multiple volumes then this reprint is of only one volume, not the whole set. This paperback book is SEWN, where the book block is actually sewn (smythe sewn/section sewn) with thread before binding which results in a more durable type of paperback binding. It can also be open wide. The pages will not fall out and will be around for a lot longer than normal paperbacks. This print on demand book is printed on high quality acid-free paper. Seller Inventory # 454159263

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Geometria indivisibilibus continuorum nova quadam ratione promota: CAVALIERI, Bonaventura

CAVALIERI, Bonaventura

Published by Duciis, Paris (1653)

Used
First Edition
Hardcover

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From: Eric Zink Livres anciens (LE VÉSINET, France)

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About this Item: Duciis, Paris, 1653. Couverture rigide. Condition: Très bon. Edition originale. Plein vélin rigide moderne. Un volume in quarto (226x166 mm), (16)-543 pages . Petit trou page 494 touchant quelques lettres Seconde édition, augmentée, du principal ouvrage de Cavalieri. Ce travail de Cavalieri sur l'utilisation des «indivisibles» ou des infinitésimaux, publié pour la première fois en 1635, constitue le premier manuel de ce qu'on appelle maintenant la méthode d'intégration. Exemplaire très frais de ce rare ouvrage Norman [I, 419 : "Cavalieri's work on the use of "indivisibles" or infinitesmals, first published in 1635, constitues the first textbook of what are now known as integration method. The work includes the statement of "Cavalieri's principle" for the determination of areas and volumes, which considers an area as made up of an indefinite number of equidistant parallel line segments, and a solid as made up of an indefinite number of parallel plane areas. Cavalieri's principle provided a simple and speedy alternative to the method of exhaustion, enabling easy calculation of such problems as the area of an ellipse and the volume of a sphere"], "Honeyman [II, 649 : "Cavalieri's chief work, celebrated for elaborating his method of indivisibles, and important as one of the works that led up to the invention of the calculus"] ___________________________________________________________________________________ ______________________________ENGLISH_DESCRIPTION______________________________ ________________________________________________________________________ ___________ Modern full stiff vellum. 4to (226x166 mm), (16)-543 pages . Small hole p. 494 touching few letters Scarce second enlarged edition Norman [I, 419 : "Cavalieri's work on the use of "indivisibles" or infinitesmals, first published in 1635, constitues the first textbook of what are now known as integration method. The work includes the statement of "Cavalieri's principle" for the determination of areas and volumes, which considers an area as made up of an indefinite number of equidistant parallel line segments, and a solid as made up of an indefinite number of parallel plane areas. Cavalieri's principle provided a simple and speedy alternative to the method of exhaustion, enabling easy calculation of such problems as the area of an ellipse and the volume of a sphere"], "Honeyman [II, 649 : "Cavalieri's chief work, celebrated for elaborating his method of indivisibles, and important as one of the works that led up to the invention of the calculus"] In quarto / 4to 1050g. Seller Inventory # E2682

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Geometria indivisibilibus continuorum nova quadam ratione promota.: CAVALIERI, Bonaventura.

CAVALIERI, Bonaventura.

Published by Heirs of Evangelista Dozza, Bologna (1653)

Used

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

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About this Item: Heirs of Evangelista Dozza, Bologna, 1653. Second edition (first, 1635) of Cavalieri?s text containing the discovery of the ?method of indivisibles?, one of the most important forerunners of the integral calculus. Book II of the work includes the statement of ?Cavalieri's principle? for the determination of areas and volumes, which considers an area as made up of an indefinite number of equidistant parallel line segments (?omnes lineae?), and a solid as made up of an indefinite number of parallel plane areas. It states that, if two planar figures are contained between a pair of parallel lines, and if the lengths of the two segments cut by them from any line parallel to the including lines are always in a given ratio, then the areas of the two planar pieces are also in this ratio (there is an analogous principle for the determination of volumes). Cavalieri?s principle provided a simple and effective alternative to the Archimedean method of exhaustion, and was used by Kepler, Galileo, Cavalieri?s pupil Torricelli, Wallis, Pascal, and others. The first edition of the Geometria is a notorious rarity, ABPC/RBH listing only the Macclesfield copy in the last 80 years. This second edition is not as rare, but is still very difficult to find in such fine condition as in our copy.?For Cavalieri a surface consists of an indefinite number of equidistant parallel straight lines and a solid of a set of equidistant parallel planes. These constitute the line and surface indivisibles respectively. For plane figures (or solids) a regula, that is, a line (or plane) drawn through the vertex, is the starting point. The regula moves parallel to itself until it comes into coincidence with a second line (or plane) termed the base or tangens opposita. The intercepts (lines or plane sections) of the regula with the original plane (or solid) figure are the elements or indivisibles making up the totality of lines (or planes) of the figure.?In the techniques developed by Cavalieri the indivisibles of two or more configurations are associated together in the form of ratios and from these ratios the relations between the areas (or volumes) of the figures themselves are derived. In moving from a relation between the sums of the indivisibles and thus to a relation between the spaces the infinite is employed, but purely in an auxiliary role.?Cavalieri?s defence of indivisible methods was based primarily on the idea of a device or artificium which works rather than on any definite or dogmatic views as to the nature of indivisibles and the spaces which they occupy. Nevertheless the classic problem of the nature of the continuum imposed itself upon him and, from the outset, he felt himself obliged to try to meet some of the arguments which he felt might be directed against his methods. He admits that some might well doubt the possibility of comparing an indefinite number of lines, or planes (indefinitae numero lineae, vel plana). When such lines (or planes) are compared, he says, it is not the numbers of such lines which are considered but the spaces which they occupy. Since each space is enclosed it is bounded and one can add to it or take away from it without knowing the actual number of lines or planes. Whether indeed the continuum consists of indivisibles or of something else neither the space nor the continuum is directly measurable. The totalities, or sums, of the indivisibles making up such spaces are, however, always comparable. To establish a relation between the areas of plane figures, or the volumes of solid bodies, it is therefore sufficient to compare the sums of the lines, or planes, developed by any regula.?The foundations for Cavalieri's indivisible techniques rest upon two distinct and complementary approaches which he designates by the terms collective and distributive respectively. In the first, the collective sums, ? l1 and ? l2, of the line (or surface) indivisibles for two figures P1 and P2 are obtained separately and then used to establish the ratio of the areas (or volumes) of the f. Seller Inventory # 4202

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