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

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6242GEOMETRIÆ

COROLLARIVM I.

QVoniam oſtendimus, tum, DC, BR, tum etiam, EF, IO, eſſe vt
ipſas incidentes, PH, NK, habetur ſimilium figurar um homo-
logas pariter eſſe, vt incidentes earundem, & oppoſitarum tangentium,
quæ ſunt earundem regulæ, quod in diffinitione aſſumitur contingere
tantum ĳs, quæ inter circuicum figurarum, & ipſas incidentes, eodem
ordine ſumptæ, continentur.

COROLLARIVM II.

PAtet etiam ex hac, & 14. huius, omnes ſimiles figuras planas poſſe
eſſe alicuius cylindrici, vel fruſti conici, oppoſitas baſes; vnde qua
pro illis in Coroll. 2. 19. huius colliguntur, pro omnibus ſimilibus figu-
ris planis etiam colligi poſſunt.

LEMMA PRO ANTECED. PROP.

SI in recta linea ſignenturtria puncta, primum, medium, & po-
ſtremum, à primo autem, & medio ducantur ad eandem par-
tem duę inuicem parallelę ita ſe habentes, vt educta à primo ad edu-
ctam à ſecundo, ſit veluti recta inter primum, & poſtremum pun-
ctum poſita, ad eam, quę inter medium, & idem poſtremum ſita eſt;
Extrema puncta parallelarum, quę non ſunt in propoſita linea, &
illius poſtremum, eruntin recta linea.

Sit propoſita recta, AC, in qua ſignatis vt-

31[Figure 31] cumque tribus punctis, C, primo, B, medio,
& , A, poſtremo, à punctis, C, B, educantur
ad eandem partem duę inuicem parallelę, quę
ſint, CE, BD, ita ſe habentes, vt, CE, ad,
BD, ſit, vt, CA, ad, AB. Dico puncta,
A, D, E, eſſe in recta linea, ſi enim (iuncta,
ED,) ipſa, ED, producta non tranſit per,
A, tranſibit ſupra, vel infra, A, ſecans, CA,
(nam, BD, eſt minor ipſa, CE, vt eſt, AB,
minor, AC,) tranſeat, vt per, M, quia igi-
tur, EDM, eſt recta erit, MCE, triangu-
lus, in quo lateri, CE, ducitur parallela, B
D, ergo trianguli, ECM, DBM, erunt æ-
114. Sexti
Elem. quianguli, & circa æquales angulos latera proportionalia, ergo, per-
mutando, CE, ad, BD, erit vt, CM, ad, MB, eſt autem vt,

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