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

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8161LIBER I. conſtructione, oſtenderemus, vt ſupra, tria latera, ΓΑ, Λ Η; AD,
HO; AB, HP; eſſe ad inuicem ſuperpoſita, vnde ſi, Λ Η, æquidi-
ſtat plano, NOP, etiam neceſſe eſſe concluderetur, Λ Η, ſeu, ΓΑ,
in ea conſtitutam, æquidiſtare plano, NOP, vel ipſi, VST, ſeu,
ΓΑ, ipſi, CDB, quod erat oſtendendum.

COROLLARIV M.

_E_X boc Lemmate colligitur ſimilium ſolidorum, iuxta Euclidis de-
finitionem, latera bomologa quœcunque, vel (duabus in ambitu
quibuſcumque figuris ſimilibus aſſumptis) iacere in plano ſimilium di-
ctarum figurarum, aut illis œquidiſtare, vel œqualiter eiſdem inclinari;
Vt in figura Lemmatis 4. ex. gr. CD, GL, (aſſumptis ſimilibus figuris,
HCD, OGL,) iacent in earum plano, BA, IF, autem vel ambo illi
œquidiſtant, vel eiſdem ſunt œqualiter inclinata, namiunctis, AC, A
11_Lemma 4._ H, FG, FO, niſi bœc ſint lateradictorum ſolidorum, fiunt anguli, BA
H, IFO, BAC, IFG, œquales, & triangula, ACH, FGO, ſimilia,
nam pyramides, ABCH, FIGO, ſunt inter ſe ſimiles, ipſa verò trian-
22_Lemma 1._ gula, ACH, FGO, œquè ad eandem partem inclinantur ipſis, HCD,
OGL, cum etiam, ACHD, FGLO, pyramides ſint ſimiles ex eodem
Lemmate 4. vnde vel, AB, FI, œquidiſtant baſibus, CHD, GOL, vel
ſunt eiſdem œqualiter inclinata, idem de cœteris bomologis quibuſcum-
que lateribus, quibuslibet ſimilibus figuris in ambitu aſſumptis compa-
ratis, pariter intelligendum erit.

LEMMA VI.

SI in ſimilibus ſolidis iuxta Euclidem ducantur plana duabus qui-
buſcumque ſimilibus figuris in eorum ambitu aſſumptis paralle-
la, quæ vt eorum baſes accipiantur; diuidant autem ducta plana eo-
rum altitudines, reſpectu dictarum baſium captas, ſimiliter ad ean-
dem partem, quęcumque latera homologa ab eiſdem ſecabuntur, ſi-
militer ad eandem partem diuidentur.

Sint in ſimilibus ſolidis iuxta Euclidis definition. 9. Vndec. Elem.
aſſumptę in ambitu duæ ſimiles figurę tanquam baſes, ex. gr. trian-
gula ſimilia, ADB, MKN, ſint verò de ambitu etiam deſcripta
triangula ſimilia, AHI, MSQ; AHD, MSK; & , IHD, QS
K; quibus etiam adiungantur latera bomologa, IF, QP, ad verti-
ces, F, P, reſpectu dictarum baſium captos, pertingentia, reliquis
dimiſſis figuris eorum ambitum complentibus, ne nimia fieret Sche-
matis confuſio, ſint autem à verticibus, F, P, demiſſæ altitudines
reſpectu baſium, ADB, MKN, ipſę, FC, PO, planis baſium

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