Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER I. L, ad, RT, vel vt, GΠ, ad, RZ, ſunt enim & ipſæ, GL, RT,
ſimiliter ad eandem partem ſectę in punctis, Π, Z, nam ſimiliter ſe-
cantur ac, FC, PO, in punctis, Λ, Γ, ergo etiam reliqua, I Π, ad,
QZ, erit vt tota, GΠ, ad totam, RZ, ideſt vt, FC, ad, PO. Eo-
dem modo oſtendemus, ΠH, ad, ZS, eſſe vt, FC, ad, PO, er-
go, IΠ, ad, QZ, erit vt, ΠH, ad, ZS, & permutando, IΠ, ad,
ΠH, erit vt, QZ, ad, ZS, ſunt ergo latera homologa, IH, QS,
ſimiliter ad eandem partem ſecta à præfatis planis, quod eodem mo-
do de quibuſcumq; homologis lateribus, quæ contingat dictis planis
ſecari, pariter oſtendemus, hoc verò demonſtrare propoſitum fuit.

112.1.

Ex Lem.
5.
0082-01
Ex Lem.
4.
19. Quin.
Elem.
Ex Lem.
5.

113. COROLLARIVM.

_E_X boc autem Lemmate inſuper habetur nedum latera bomologa ſi-
milium ſolidorum, ſed etiam, ſi illa producantur vſq; ad oppoſita
tangentia plana, eorum reſidua, vel ipſa tota, eſſe vt eorum dictas al-
titudines.

114. THEOREMA XXVI. PROPOS. XXIX.

SI in duobus ſimilibus ſolidis iuxta defin. 9. vndec. Elem. accipiantur, ac in eorumdem ambitu, duæ quæcumq; ſimiles figurę planę tanquam baſes, quibus parallela ducan-
tur quæcumq; plana eadem ſecantia, necnon corum altitu-
dines, reſpectu dictarum baſium aſſumptas, ſimiliter ad ean-
dem partem diuidentia. Productæ ijſdem in ſolidis figuræ
ſimiles erunt iuxta definitionem 10. huius, & omnium ho-
mologæ duabus quibuſdam regulis æquidiſtabunt.

Sint ſimilia ſolida iuxta defin. 9. vndec. Elem. ipſa, AEFSOGo,
Tl & p f8s, in eorum autem ambitu capiantur ſimiles quæcumque
figurę planę, OGFS, f8 & p, quibus parallela ducantur duo quę-
cumque plana eadem ſecantia, necnon & altitudines reſpectu dicta-
rum baſium aſſumptas ſimiliter ad eandem partem diuidentia, ac in
ipſis ſolidis figuras, LHMP, YVZd, producentia. Dico has eſſe
ſimiles figuras planas icxta defin. 10. huius, omniumque ſic produ-
ctarum in dictis ſolidis homologas duabus quibuſdam regulis, vtex. gr. ipſis, OS, fp, æquidiſtare. Igitur figurarum ambientium dicta
ſolida duæ aliæ ſimiles quæcumq; capiantur cum baſibus concurren-
tes, vt ex. gr. oOS, sfp, ſimilia triangula, ducantur autem pręfa-
tis baſibus oppoſita tangentia plana, AC, TR, ſecantia producta

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