Ceva, Giovanni - Geometria motus

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PROP. XVII. THEOR. XIII.

IIſdem manentibus. Dico triangula ACB, LHM eſſę
ſimilia. Sunt enim parallelæ &c. interſe tam rectæ CB,
ML, quàm CA, MH; ideo anguli ACB, HML interſe
æquabuntur, & ſunt circa eos proportionalia latera, nem.
pe BC ad CA, vt LM, MH; ergo conſtat propoſitum.

Corollarium.

Simul conſtat rectas AB, LH interſe æquidiſtare.

PROP. XVIII. THEOR. XIV.

IIſdem vt ſupra manentibus, ita tamen vt ACD ſit an
gulus rectus (ſic enim DC perpendicularis erit duabus
AC, CB) Dico ſolidum huiuſmodi ad priſma, cuius baſis
ABC, & altitudo CD eandem habere rationem, quam ſo
lidum rotundum ortum ex rotatione figuræ CAD circą
axem CD ad cylindrum genitum ex conuerſione rectan
guli AC in CD circa eundem axem.

Tab. 6. Fig. 8.

Compleatur ipſum priſma, & ſit quidem AQDPBC,
quod ſecetur vnà cum propoſito ſolido per quoduis pla
num baſi ACB æquidiſtans: fiet in priſmate ſectio trian
gulum OMN ſimile, æqualeque ipſi ACB, & in altero ſo
lido triangulum LHM eidem ACB ſimile. Triangulum
ACB priſmatis ad triangulum idem ſolido propoſito com
mune, eſt vt circulus radio CA deſcriptus ad circulum
eundem; Item triangulum NOM ſectio priſmatis eſt ad
triangulum LHM ſectionem propoſiti ſolidi, vt circulus ex
radio MO deſcriptus ad circulum radio MH. Cum dein
de idem dicatur de alijs omnibus ſectionibus priſmatis, &

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