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

316[Figure 316] circumferentia, MSE, ad circumferentiam, ITV, eſt vt quadratũ
EA, ad quadratum, AV, ideſt vt, RQ, ad, XG, eſt autem, RQ, æ,
qualis circumferentiæ, MSE, ergo & , GX, circumferentiæ, ITV,
æqualis erit, & ſic oſtendemus quamlibet circumferentiam ipſi
A, concentricam, & interceptam inter ſpiralem, AIE, & rectam
AE, tamen extra ſpatium helicum, AIE, adæquari ductæ in trili-
neo, OGRQ, ipſi, RQ, ductæ parallelæ, quæ nempè abſcindunt
verſus puncta, O, A, ipſarum, OQ, AE, partes ęquales, & quia,
OQ, AE, ſupponuntur æquales, ideò omnes lineę trilinei, OGR
Q, regula, RQ, omnibus circumferentijs trilinei recta, AE, ſpira-
li, AIE, & circũferentia, MSE, cõpręhenſi æquales erunt. Similiter,
quia eſt, RQ, ad, NX, vt, QO, ad, OX, vel, EA, ad, AV, vel circũ-
ferentia, MSE, ad, TIV, æquatur autem, RQ, ipſi, MSE, ergo, N
X, æquatur circumferentiæ, TIV, & ſic oſtendemus omnes lineas
trianguli, ORQ, adæquari omnibus circumferentijs circuli, MSE,
ergo vt trianguli, ORQ, omnes lineæ ad omnes lineas trilinei, OG
RQ, vel vt triangulum, ORQ, ad trilineum, OGRQ, ita omnes
113. l. 2.

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