Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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127107LIBER II. dem plano, & in eadem altitudine, quæ ſint, BCDA, ADE, ſit
autem altitudo figuræ, ABCD, ſumpta reſpectu ipſius rectæ, CD,
& altitudo figuræ, ADE, reſpectu ipſius, DE, quæ intelligantur
abſcindere ex eadem parte à communi altitudine partes æquales,
quæ ſibi in directum erunt, ſint verò ambæ communis regula om-
nium linearum dictarum figurarum, & ſit ducta alia vtcumq; ei-

69[Figure 69] dem, CE, parallela, MN,
cuius portio manens in figu-
ra, BD, ſit, MO, & ma-
nens in figura, ADC, ſit,
ON; rectangula igitur, C
DE, MON, & reliqua re-
11_Definit. i._
_huius._ ctangula, quæ ſub qualibet
earum, quæ dicuntur omnes lineæ figuræ, BD, (regula, CE, vel,
CD,) & illi in directum poſita in figura, ADE, continentur (erit
autem ſemper aliqua eidem in directum, præterquam fortè illi, qua
tangit figuram, vt, BA, potest . n. in figura, ADE, illi vice lineæ
vnum punctum tantum reſpondere, vt, A, hoc tamen rect augulum
non computatur, quia nihil illis adiungit, erit inquam bæc linea-
rum reſpondentia in figura, ADE, eis, quæ ſumuntur in, BD, nam
ſunt in eadem altitudine ſumpta aſpectu earundem linearum, ſub
quibus rectangula continentur) ſimul ſumpta vocamus: Rectangu-
22_D. Def. 8._
_huius._ la ſub figuris, BCDA, ADE.

Siverò contingeret alteram earundem ſigurarum eſſe par allelo-
grammum, & regulam omnium eiuſdem linearum eſſe vnum eiu-
ſdem laterum, vt, CD, reſpectu cuius ſumitur altitudo, tune quia
illæ, quæ æquidiſtantipſi, CD, in parallelogrammo, BD, ſunt ei-
dem, CD, æquales, & ſunt latera dictorum rectangulorum, ideò
dico, nos ea vocare poſſe nedum rectangula ſub his figuris, ſed etiam
ſic appellare, nempè. Omnia rectangula figuræ ADE, (quæ non,
eſt neceſſariò parallelogrammum) æquè alta, ac vnum eorum . i. ac
rectangulum, CDE, altitudinis ſcilicet æqualis ipſi, CD, prout
libuerit autem nominentur.

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