Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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AE, ED, ſint, MO, OQ, & </
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periamus, MO, ad, OI, eſſe vt, QO, ad, OP. </
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xml:space
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neas, AE, ad omnes lineas figurę, BCE, eſſe vt omnes lineę, BF,
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ad omnes lineas figuræ, B E F, ſi verò vice linearum comparentur
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ab eiſdem deſcriptę figurę, ſimi-
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libus exiſtentibus, quę ab omni-
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bus lineis vniuſcuiuſque propo-
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ſitarum figurarum deſcribuntur,
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cuius deſcribentes ſint earum li-
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neę, vel latera homologa. </
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<
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co omnes figuras ſimiles ipſius,
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A E, ad omnes figuras ſimiles
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ſigurę, BCE, eſſe vt omnes fi-
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guras ſimiles ipſius, BF, ad omnes figuras ſimiles figuræ, BEF,
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quia enim, MQ, vtcunque ducta eſt parallela ipſi, CF, & </
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<
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xml:space
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O, ad, OI, vt, QO, ad, OP, permutando erit, vt, MO, ad, O
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Q, ſic, IO, ad, OP, i. </
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<
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<
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<
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oſtendemus, vt, CE, ad, EF, ita eſſe quaſlibet alias duas in figu-
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ris, BCE, BEF, exiſtentes ipſi, CF, parallelas, & </
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ſic omnia ad omnia .</
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xml:space
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huius.</
note
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CE, ad omnes lineas figurę, BEF, vt autem, CE, ad, EF, ita ſunt
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omnes lineæ, AE, ad omnes lineas, ED, ergo omnes lineę, AE,
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ad omnes lineas, ED, erunt vt omnes lineę figurę, BCE, ad om-
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nes lineas figuræ, BEF.</
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<
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figuras, ex. </
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cuius latus, IO, ita reperiamus eſſe circulum, cuius diameter, OQ,
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ad polygonum, cuius latus, OQ, omnium autem linearum, AE,
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fingulæ deſcribant quadrata, & </
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ſingulę deſcribant, triangula &</
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<
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ſingulæ deſcribant circulos, & </
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lygona prædicto ſimilia, ita vt quæ in eadem figura ſunt lineæ, vel
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tando, ad circulum, OQ, ita triangulum &</
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lygonum, OP, quia verò, MO, &</
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<
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EF, ideò quadratum, MO, &</
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note
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ita erit triangulum &</
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<
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quia, MQ, vtcunq; </
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nia quadrata, AE, ad omnes circulos, BF, eſſe, vt omnia triangu-
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la &</
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ius.</
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BEF, & </
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