Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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vt figura tertiæ ad figuram quartæ. </
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<
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xml:space
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">Et ſi fuerint quatuor fi-
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guræ planæ proportionales, ita vt quæ ſunt termini eiuſdem
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proportionis ſint figuræ ſimiles, deſcriptæ ab eorundem li-
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neis, vel lateribus homologis; </
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<
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">lineæ, vel latera homologa
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deſcribentia erunt proportionalia.</
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<
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<
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xml:space
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prima verò, & </
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<
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<
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xml:space
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">planas ſimiles, AXB, CVD,
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0152-01
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&</
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<
s
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xml:space
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">, FG, HM, ſimiles figuras pla-
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nas, FOG, HNM, licet prędictis
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diſſimiles eſſent, & </
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<
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figurarum deſcriptarum lineæ, vel
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latera homologa. </
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<
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xml:space
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">Dico, AXB, ad,
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CVD, eſſe vt, FOG, ad, HNM.
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</
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<
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rum, AB, CD, &</
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<
s
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xml:space
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portionalis ipſarum, FG, HM; </
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<
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igitur, AXB, ad, CVD, vt, AB,
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ad, R, .</
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<
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">i. </
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<
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">in ratione dupla eius, quam habet, AB, ad, CD, .</
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">i. </
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<
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antec.</
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quam habet, FG, ad, HM, .</
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<
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<
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xml:space
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">vt, FG, ad, I, quę eſt, vt, FOG,
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ad, HNM, ergo vt, AXB, ad, CVD, ita erit, FOG, ad, H
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NM.</
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<
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HNM, ſibi ſimilem, licet iſtæ eſſent prædictis diſſimiles, & </
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<
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ſcribentes ſint earum lineæ, vel latera homologa. </
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<
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xml:space
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<
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CD, eſſe vt, FG, ad, HM, ſit adhuc, R, tertia proportionalis ip-
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ſarum, AB, CD, &</
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<
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xml:space
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">, I, tertia proportionalis ipſarum, FG, HM,
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<
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xml:space
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antec.</
note
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eſt ergo, vt figura, AXB, ad, CVD, ita, AB, ad, R, vt verò fi-
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gura, FOG, ad, HNM, ita, FG, ad, I, eſt verò, vt, AXB, ad,
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CVD, ita, FOG, ad, HNM, ergo vt, AB, ad, R, ſic, FG, ad,
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I, eſtautem, AB, ad, R, dupla rationis ipſius, AB, ad, CD, &</
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<
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FG, ad, I, dupla rationis ipſius, FG, ad, HM, ergo vt, AB, ad,
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CD, ita, FG, ad, HM, quæ oſtendere opus erat.</
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<
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">_P_Ropoſitionis proximè ſubſequentis nimia fortaſſe prolixitas faſti-
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dium potius Lectori, quam delectationem pariet, veruntamen, qui
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hoc veretur, ac tantum otij, aut tolerantiæ habere nequit, vt illius ſa-
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tis tongam texturam percurrere Valeat, ipſam ſupponat, ac prætereat,
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ijs enim præcipuè à me dirigitur, quibus nec otium deeſt, nec </
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