Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VI.
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ſpatium, OP℟, erit vt omnia quadrata, MG, regula, MI, ad om-
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nia quadrata trianguli, TLC, eſt autem idem ſector, AOQ, ad ſpa-
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tium, OP℟Q, vt omnia quadrata, MG, ad omnia quadratatrian-
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guli, MIC, regula eadem, ergoſector, AOQ, ad reliquum ſpa-
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tium, dempto ſpatio, OP℟, à ſpatio, OP℟Q, erit vt omnia qua-
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drata, MG, regula, MI, ad omnia quadrata trapezij, MILT, ſed
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xml:space
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hæcſunt, vt quadratum, GT, adrectangulum, GTL, cum {1/3}. </
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drati, LG, ergo, conuertendo, ſpatium, ℟OQ, ad ſectorem, AOQ,
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erit vtrectangulum, AO℟, cum tertia parte quadrati, A℟, ad qua-
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dratum, AO, quod erat oſtendendum.</
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">IN eadem antecedentis ſigura centro, O, diſtantia, O℟,
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deſcripta circumferentia, ℟Y, oſtendemus trilineum,
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A℟Q, ad trilineum, ℟QY, eſſe vt, ℟O, cum {2/3}. </
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">℟A, ad, ℟
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O, cum tertia parte ipſius, ℟A.</
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">Quia enim ex antecedenteſector, AOQ, ad ſpatium, Q℟O, eſt
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vt quadratum, AO, ad rectangulum, AO℟, cum {1/3}. </
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<
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xml:space
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">quadrati, A ℟,
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per conuerſionem rationis, idem ſector ad trilineum, A℟Q, erit vt
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quadratum, AO, ad rectangulum, O℟A, cum {2/3}. </
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<
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xml:id
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xml:space
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">quadrati, ℟A, nã
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dempto rectangulo, AO℟, à quadrato, AO, remanet rectangulũ,
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OA℟,. </
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<
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">i. </
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<
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">rectangulũ, O℟A, cum quadrato, ℟A, à quo ablato {1/3}. </
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<
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manet rectangulum, O℟A, cum {2/3}. </
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<
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xml:space
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">quadrati, ℟A, ideſt cum re-
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">1. Secundi
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Elem.</
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ctanguloſub {2/3}. </
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">ſub, ℟A, quod cum rectangulo, O℟A, cõ-
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ficit rectangulum ſub compoſita ex, O℟, & </
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">{2/3}. </
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">℟A, & </
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conuertendo igitur trilineum, A℟Q, ad ſectorem, AOQ, erit vt
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xlink:label
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">Coroll. 2.
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3. huius.</
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rectangulum ſub compoſita ex, O℟, & </
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<
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">ſub, ℟A, ad qua-
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dratum, OA, inſuper ſector, AOQ, ad ſectorem, ℟OY, eſt vt qua-
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dratum, AO, ad quadratum, O℟, & </
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<
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xml:space
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">quia idem ſector, AOQ, ad
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ſpatium, Q℟O, eſt vt quadratum, AO, ad rectangulum, AO℟, cũ
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{1/3}. </
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<
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">quadrati, ℟A, ideò ſector, AOQ, ad reliquum dempto à ſpatio,
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℟OQ, ſectore, ℟OY, ideſt ad trilineum, Q℟Y, erit vt quadratu,
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Elem.</
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AO, ad reliquum rectanguli, AO℟, cum {1/3}. </
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dempto quadrato, ℟O, ideſt ad rectangulum, O℟A, cum {1/3}. </
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drati, ℟A, erat autem trilineum, A℟Q, ad rectorem, AOQ, vt re-
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ctangulum ſub compoſita ex, O℟, & </
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">℟A, ad quadratum, AO,
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ergo ex æquali trilineum, A℟Q, ad trilineum, ℟QY, erit vt rectã-
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gulum ſub compoſita ex, O℟, & </
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<
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lum, O℟A, cum 3. </
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