Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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rallelæ, ex quò ſi iungatur MZ, & </
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<
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">parallelæ erunt, & </
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<
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facta conſtructione vt ſupra, idem omninò demonſtrabitur, nempe interce-
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ptam YX minorem adhuc eſſe ipſa DS. </
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<
s
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xml:space
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">Huiuſmodi igitur Parabolæ con-
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gruentes, quò magis à tangente EA remouentur ad ſe propiùs accedunt:
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</
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<
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<
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head
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<
s
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">SEd hoc idem aliter in nouo hoc ſchemate, in quo item oſtendetur inter-
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ceptam contingentem EA maiorem eſſe intercepta applicata DI, & </
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<
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">DI
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maiorem infra intercepta
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0097-01
"/>
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ML, & </
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<
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">hoc ſemper, ſi ſectio-
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nes in infinitum producan-
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tur. </
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<
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">Ducta enim DN paral-
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lela ad EB, eadem penitus
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methodo, qua ſuperiùs vſi
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ſumus, demonſtrabimus DN
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ipſi EB æqualem eſſe, & </
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rallelam, quare, & </
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<
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ctæ BN, ED æquales erunt,
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ac parallelæ: </
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<
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">ſi ergo BN ſe-
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cetur bifariam in O, duca-
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turque POT diametro BE
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æquidiſtans, patet ipſam
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TOP eſſe vtriuſque
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mi conic.</
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bolæ diametrum, & </
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vnam ei applicatarum in
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Parabola ABC, vti etiam QDER ipſi NB æquidiſtantem: </
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<
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& </
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">PR æquales erunt, ſed eſt DP æqualis PE (ob parallelas, & </
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<
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">quia NO
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æquatur OB) quare reliquæ QD, ER æquales erunt, ideoque rectangulum
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QDR æquabitur rectangulo QER. </
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<
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">Ampliùs ducatur TV æquidiſtans ad
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QR, vel ad NB: </
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<
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<
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mi conic.</
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occurrere in V, (nam hæc, cum ſecet in B alteram parallelarum BN, ſecat
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quoque reliquam TV.) </
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<
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">Cumque duæ rectæ TV, BV, ſectionem ABC con-
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tingentes, in vnum conueniant, ſitque QR ipſi TV, atque IS, & </
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">AC ipſi BV
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æquidiſtantes, ac ſe mutuò ſecantes in D, & </
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">E, erit rectangulum QDR ad
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IDS, vt quadratum TV ad BV quadratum, itemque rectangulum QER
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conic.</
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AEC, vt idem quadratum TV ad BV, quare vt rectãgulum QDR ad
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">ibidem.</
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ita rectangulum QER ad AEC, & </
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">permutando rectangulum QDR ad QER,
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vt rectangulum IDS ad AEC, ſed QDR, QER ſunt ęqualia, vt modò oſten-
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dimus, ergo & </
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<
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">rectangulum IDS æquatur rectangulo AEC, ſiue quadrato
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AE, quare vt SD ad EA, ita EA ad DI, ſed SD maior eſt EA, cum ſit
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maior CE ſiue EA, vnde AE quoque, maior erit DI. </
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<
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detur rectangulum LMX æquale quadrato AE: </
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<
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">vnde rectangula IDS, LMY
<
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inter ſe æqualia erunt, ſed eſt latus MY maius later@ DS, cum eius ſegmen-
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tum ZY maius ſit huius ſegmento XS, & </
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<
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reliquo ſegmento DX, quare latus LM minus erit latere ID, & </
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