Bologna, Giacomo Monti, 1647
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.
First edition, 4to, (23 x 16.2 cm); [12], 543, [1] pp., woodcut device on title page, woodcut head- and tailpieces and initials, woodcut diagrams throughout the text, some light spotting throughout; bound in 18th-century calf with gilt lettering and impressions on the spine, red speckled edges, boards detached but present.
First edition, 4to, (23 x 16.2 cm); [12], 543, [1] pp., woodcut device on title page, woodcut head- and tailpieces and initials, woodcut diagrams throughout the text, some light spotting throughout; bound in 18th-century calf with gilt lettering and impressions on the spine, red speckled edges, boards detached but present.
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