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

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124104GEOMETRIÆ guris iuxta regulas eas, quę ſunt regulę omnium ſimilium fi-
gurarum earundem propoſitarum genitricium figurarum, di-
centur ſolida inter ſe, vel ad inuicem ſimilaria, genita ex di-
ctis figuris iuxta dictas regulas, vel intelligentur ſemper eſſe
inter ſe, ſeu ad inuicem ſimilaria, licet hoc non exprimatur,
quotieſcunq; contrarium aliquid non adijciatur.

11D.

Cum autem duas figuras in eodem plano habuerimus in
eadem altitudine exiſtentes, rectangula ſub ſingulis earum,
quæ dicuntur omnes lineæ vnius propoſitarum figurarum, &
illis in directum reſpondentibus in alia figura ſimul ſumpta
ſic vocabimus, nempè Rectangula ſub eiſdem figuris, regu-
la eadem, quæ eſt omnium ſumptarum linearum regula.

22E.

Cum verò propoſitarum figurarum altera fuerit parallelo-
grammum, cuius baſis, iuxta quam altitudo ſumitur, ſit ſum-
pta pro regula, dicta rectangula vocabuntur etiam: Omnia
rectangula reliquæ figuræ æquè alta ac eorum vnum.

APPENDIX.

Pro antecedentium Definitionum explicatione.

_S_It ſigura plana quæcunque, ABC, duæ eiuſdem oppoſitæ tan-
gentes vtcunque ductæ, EO, BC, intelligantur autem per, E
33_Coroll.i._
_lib.I._ O, BC, indefinitè extenſa duæ plana inuicem parallela, quorum
quod tranſit per, EO, ex. gr. moueatur verſus planum per, BC,
ſemper illi æquidiſtans, donec illi congruat, igitur communes ſe-
ctiones talis moti, ſiue fluentis plani, & figuræ, ABC, quæ in toto
motu ſiunt, ſimul collectæ à me vocantur: Omnes lineæ figuræ, AB
44_Defin.1._
_huius._ C, quarum aliquæ ſint ipſæ, LH, PF, BC, ſumptæ regula earum
vna, vt, BC, recti tranſitus, cum plana parallela rectè ſecant fi-
guram, ABC, eiuſdem obliqui tranſitus, cum illam obliquè ſecant,
eius ſcilicet tranſitus, qui in tali inclinatione ſit.

Intelligamus nunc, ABC, eſſe ſolidum, cuius duo oppoſita pla-
na tangentia ſint, quæ tranſeunt per, EO, BC, moueatur autem
adhuc planum, per, EO, extenſum, verſus planum per, BC,

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