Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ergo intra, EB, vtcumque punctum, C, & </
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<
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xml:space
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P, parallela, CM, ſecans curuam circuli, vel ellipſis, EDRP, in,
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N; </
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<
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xml:space
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<
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rectangulum, RBE, ad rectangulum, RCE; </
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<
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xml:space
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rallelogrammum in eadem baſi, & </
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<
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tudine, cum ſemiportione, EBP, regu-
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la eſt ipſa baſis, &</
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<
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xml:space
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">, CM, ducta vtcum-
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que parallela ipſi baſi, repertumque eſt
<
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/>
quadratum, CM, ad quadratum, CN,
<
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eſſe vt rectangulum, RBE, ad rectan
<
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gulum, RCE, ergo magnitudines ho-
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rum quatuor ordinum erunt proportio-
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nales.</
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<
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xml:space
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<
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xml:space
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xlink:label
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xml:space
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<
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26.lib. 2.</
note
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mi, EP, magnitudines primi ordinis col-
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lectæ, iuxta primam, nempè iuxta qua-
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dratum, CM, ad omnia quadrata ſemi-
<
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portionis, EBP, magnitudines ſecundi
<
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ordinis collectas, iuxta ſecundam. </
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<
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<
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ta quadratum, CN, erunt vt rectangu-
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la ſub maximis abſciſſarum, EB, & </
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<
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adiunctis, BR, magnitudines tertij or-
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dinis collectæ, iuxta tertiam .</
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<
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<
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ctangulum, RBE, ad rectangula ſub
<
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omnibus abſciſſis, EB, & </
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<
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xml:space
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">reſiduis earun-
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dem, adiuncta, BR, (recti, vel obliqui
<
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tranſitus ſupradictis exiſtentibus) quæ
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ſunt magnitudines quarti ordinis colle-
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ctæ, iuxta quartam.</
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<
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<
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R CE; </
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<
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maximis abſciſſarum, EB, & </
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ctis, BR, ad rectangula ſub omnibus ab-
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ſciſſis, EB, adiuncta, BR, & </
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<
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reſiduis, ſunt vt, BR, ad compoſitam ex
<
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<
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position
="
left
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xlink:label
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note-0218-02
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xlink:href
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xml:space
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">Cor. 30.
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lib.2.</
note
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dimidia, BR, & </
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<
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">ſexta parte, EB, ergo conuertendo omnia quadrata
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ſemiportionis, BEP, ad omnia quadrata parallelogrammi, EP, vel
<
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<
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xlink:label
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note-0218-03
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xlink:href
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xml:space
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">8. lib. 2.</
note
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iſtorum quadrupla .</
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<
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<
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">omnia quadrata portionis, DEP, ad omnia
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quadrata parallelogrammi, FP, erunt vt compoſita ex, {1/6}, BE, &</
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<
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{1/2}, BR, ad eandem, BR; </
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<
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<
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<
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xml:space
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">Dico vlterius omnia quadrata portionis, EDP, ad omnia qua-
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drata trianguli, DEP, eſſe vt compoſita ex dimidia totius, ER, & </
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<
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ipſa, BR, ad eandem, BR. </
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drata parallelogrammi, FP, ad omnia quadrata portionis, </
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