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CAVALIERI, Bonaventura (1598-1647). Exercitationes geometricae sex. Bologna: Jacob Monti, 1647.
4° (218 x 160mm). Half-title, woodcut device on title, woodcut diagrams and illustration of a water-well, initials, head- and tailpieces, letterpress folding table, replacement diagram pasted over that on p.90. (Some light dampstaining, tiny single wormhole in margin of first 50 leaves and in few others, wormtrack with some loss in following 40 leaves, folding table also affected by small wormtrack, occasional light browning and spotting.) Old vellum, new endpapers (extensively restored, some staining, lightly bowed).
RARE FIRST EDITION of Cavalieri's second work on integration methods, an appendix and elaboration of his Geometria indivisibilibus (1635) and one of the most important forerunners of the integral calculus. The method of indivisibles was used by Galileo, Pascal, Cavalieri's pupil Torricelli, Wallis and others. The present work contains numerous applications of the method, as well as replies to those who criticised the earlier work. The method of indivisibles 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. The sixth exercitatio describes a hydraulic pump which Cavalieri designed for the monastery of S. Maria della Mascarella in Bologna, where he held the honorary position of prior. Brunet I, 1697 ('ouvrage très-recommandable'); Honeyman 649; Sotheran I, 734 ('containing the earliest demonstration of the theorems of Pappus, and the first determination of focal distances of glass lenses'); Riccardi I, 329 (‘una delle più preziose opere del nostro autore’).
4° (218 x 160mm). Half-title, woodcut device on title, woodcut diagrams and illustration of a water-well, initials, head- and tailpieces, letterpress folding table, replacement diagram pasted over that on p.90. (Some light dampstaining, tiny single wormhole in margin of first 50 leaves and in few others, wormtrack with some loss in following 40 leaves, folding table also affected by small wormtrack, occasional light browning and spotting.) Old vellum, new endpapers (extensively restored, some staining, lightly bowed).
RARE FIRST EDITION of Cavalieri's second work on integration methods, an appendix and elaboration of his Geometria indivisibilibus (1635) and one of the most important forerunners of the integral calculus. The method of indivisibles was used by Galileo, Pascal, Cavalieri's pupil Torricelli, Wallis and others. The present work contains numerous applications of the method, as well as replies to those who criticised the earlier work. The method of indivisibles 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. The sixth exercitatio describes a hydraulic pump which Cavalieri designed for the monastery of S. Maria della Mascarella in Bologna, where he held the honorary position of prior. Brunet I, 1697 ('ouvrage très-recommandable'); Honeyman 649; Sotheran I, 734 ('containing the earliest demonstration of the theorems of Pappus, and the first determination of focal distances of glass lenses'); Riccardi I, 329 (‘una delle più preziose opere del nostro autore’).
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