Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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habet rationem compoſitam ex ratione trianguli, LQΣ, ad trian-
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gulum, L&</
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19. l. 2.
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33. Sexti
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Elem.</
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ferentiæ, CDFBC, ad circumferentiam, CDFB, quia prædictis æ-
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quatur ideſt ex ratione circuli, CDFB, ad ſectorem, vel eius reſi-
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duum, ACDFBA, & </
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LZ {13/ }, ideſt ex ratione quadrati, PL, ad quadratum, L4, ideſt ex ra-
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19. l. 2.</
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tione quadrati, BA, ad quadratum, AK, ideſt ex ratione ſectoris
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(dicatur ſic breuitatis cauſa, ſiue ſit ſector, ſiue eius reſiduum) AC
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DFB, ad ſectorem, AIR εkA, quæ duæ rationes componunt ratio-
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3. huius.
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Defin. 12.
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l. 1.</
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nem circuli, CDFB, ad ſectorem, AIR εKA, ergo triangulus, LQ
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Σ, ad triangulum, LZ {13/ }, erit vt circulus, CDFB, ad ſectorem, AI
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RεKA, ſed triangulus, LQΣ, eſt æqualis circulo, CDFB, ergo triã-
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gulus, LZ {13/ }, ſectori, AIR εKA, æqualis erit, & </
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<
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">eſt trilineus, LΖΩ,
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huius.</
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æqualis ſpatio, AISMGA, ergo ſector, AIR εKA, ad ſpatium, AIS
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MGA, erit vt triangulus, LZ {13/ }, ad trilineum, LΖΩ, .</
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tum, 4L, ad rectangulum ſub, 4L, Lβ, cum {1/3}. </
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dratum, IA, ad rectangulum, ſub, IA, AG, cum {1/3}. </
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quod erat oſtendendum.</
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