Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ AE, ED, ſint, MO, OQ, & interceptę figuris ſint, IO, OP, le-
periamus, MO, ad, OI, eſſe vt, QO, ad, OP. Dico omnes li-
neas, AE, ad omnes lineas figurę, BCE, eſſe vt omnes lineę, BF,
ad omnes lineas figuræ, B E F, ſi verò vice linearum comparentur
ab eiſdem deſcriptę figurę, ſimi-
libus exiſtentibus, quę ab omni-
bus lineis vniuſcuiuſque propo-
ſitarum figurarum deſcribuntur,
cuius deſcribentes ſint earum li-
neę, vel latera homologa. Di-
co omnes figuras ſimiles ipſius,
A E, ad omnes figuras ſimiles
ſigurę, BCE, eſſe vt omnes fi-
guras ſimiles ipſius, BF, ad omnes figuras ſimiles figuræ, BEF,
quia enim, MQ, vtcunque ducta eſt parallela ipſi, CF, & eſt, M
O, ad, OI, vt, QO, ad, OP, permutando erit, vt, MO, ad, O
Q, ſic, IO, ad, OP, i. vt, CE, ad, EF, ſic, IO, ad, OP, & ſic
oſtendemus, vt, CE, ad, EF, ita eſſe quaſlibet alias duas in figu-
ris, BCE, BEF, exiſtentes ipſi, CF, parallelas, & vt vna ad vnam
ſic omnia ad omnia . i. vt, CE, ad, EF, ita omnes lineæ figurę, B
CE, ad omnes lineas figurę, BEF, vt autem, CE, ad, EF, ita ſunt
omnes lineæ, AE, ad omnes lineas, ED, ergo omnes lineę, AE,
ad omnes lineas, ED, erunt vt omnes lineę figurę, BCE, ad om-
nes lineas figuræ, BEF.

248.1.

0181-01
0182-01
Coroll. 4.
huius.

Si verò vice linearum ſumamus deſcriptas, vt dictum eſt, ab eiſdem
figuras, ex. gr. ſi, vt quadratum, MO, ad triangulum & ae; quilaterum,
cuius latus, IO, ita reperiamus eſſe circulum, cuius diameter, OQ,
ad polygonum, cuius latus, OQ, omnium autem linearum, AE,
fingulæ deſcribant quadrata, & omnium linearum figuræ, BCE,
ſingulę deſcribant, triangula & ae; quilatera, & omnium linearum, BF,
ſingulæ deſcribant circulos, & figuræ, B E F, ſingulę deſcribant po-
lygona prædicto ſimilia, ita vt quæ in eadem figura ſunt lineæ, vel
latera deſcribentia ſint homologa, erit vt quadratum, MO, permu-
tando, ad circulum, OQ, ita triangulum & ae; quilaterum, IO, ad po-
lygonum, OP, quia verò, MO, & ae; quaturipſi, CE, & , OQ, ipſi,
EF, ideò quadratum, MO, & ae; quatur quadrato, CE, & circulus,
OQ, circulo, EF, & ideò, vt quadratum, CE, ad circulum, EF,
ita erit triangulum & ae; quilaterum, IO, ad polygonum, OP, vnde,
quia, MQ, vtcunq; ducta eſt parallelaipſi, CF, concludemus om-
nia quadrata, AE, ad omnes circulos, BF, eſſe, vt omnia triangu-
la & ae; quilatera figuræ, BCE, ad omnia polygona vni ſimilia figuræ,
BEF, & permutando omnia quadrata, AE, ad omnia triangula a-

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