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

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8767LIBER I. uX, oſtenderemus figuras his ductis comprehenſas, quales fuerunt,
LPIK, YdXu, eſſe ſimiles, ex quo propoſitum quoque noſtrum
haberemus. Similiter ſi anguli ſolidi, Q, f, pluribus, quam tribus
angulis planis contineantur, currit tamen demonſtratio, cum trian-
11Ex Lem.
4. & 1. gula, GOo, 8fs, licet non ſint in ambitu ſolidorum ſint tamen ſi-
milia, & ęquè ad eandem partem inclinata figuris, cum quibus con-
currunt, etenim ex. gr. pyramides, SGOo, p8fs, ſi eorum latera
iungerentur, ſimiles eſſent, quapropter ipſius demonſtrationis vis
non eneruatur. Similiter ſi, oOS, sfp, non eſſent triangula, ſed
aliæ quæcumque figuræ ſimiles, pro, oS, sp, acceptis lateribus ip-
ſis, Oo, fs, adiuncta, os, conterminantibus, & planis ad hæc la-
tera pariter terminantibus, eodem modo demonſtratio abſoluere-
tur: hæc omnia autem ſingillatim proſequi nimis longum, ac ſche-
matibus rem aperire, res tricis plena eſſet, quapropter Lectoris in-
duſtriæ hoc relinquo, ſi enim ea rectè percepcrit, quę ſuperius expli-
cata ſunt, circa huius veritatem minimè hæſitabit, infinita autem ſi-
milium ſolidorum planis contentorum varietas efficit, vt ægrè ip-
ſius demonſtrationis vniuerſalitatem oculis ſubijcere poſſim, quod
Lector æqui, bonique faciat, hæc verò oſtendenda proponebantur.

THEOREMA XXVII. PROPOS. XXX.

POſita definit. 9. vndec. Elem. ſimilium ſolidarum figura-
rum, ſequitur, & mea definitio generalis ſimilium ſo-
lidorum.

Aſſumptis denuò antec. Propoſ. figuris, ſint adhuc ſimilia ſolida
iuxta Euclidem ipſa, AGS, T8p. Dico eadem eſſe etiam ſimilia
iuxta definit. 11. huius, quam de ſimilibus ſolidis generaliter attuli.
Sint autem ducta eadem oppoſita tangentia plana, vt ibi, ita vt duę
ſimiles figurę, GFSO, f8 & p, ſint plana contactuum ex vna par-
te, ex alia verò ſint plana tangentia, AC, TR, captis autem alijs
duabus ſimilibus figuris cum baſibus concurrentibus, ipſis nempè, O
So, fps, illarum plana extendantur, ita vt ſecent oppoſita tangen-
tia plana, in rectis nempè, BC, OD; QR, f℟; extenſis autem vl-
terius planis, GOo, 8fs, quęnunc ſint in ambitibus ſolidorum ipſa
ſecent oppoſita tangentia plana in rectis, AB, TQ; GO, 8f, &
plana figurarum, OSO, fps, producta in rectis, BO, Qf, ſecen-
tur verò hęc ſolida duobus planis oppoſitis tangentibus parallelis vt-
cumque, & ſint illa eadem, quę in ſolidis produxerunt figuras, LH
MP, YVZd, iſtæ ergo ſimiles erunt, & earum homologæ, ſi

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