Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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quare angulus D A M, ſiue in ſimili triangulo D L I, angulus D L I erit
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maior angulo A H M, ſiue angulo parallelarum externo I B L: </
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tur in triangulo I B L ſit angulus I B L minor I L B, erit latus I L minus
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latere I B.</
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<
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gula A P O, B P H
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conic.</
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æqualia, addito commu-
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ni triangulo A P B, erunt
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triangula A O B, A H B
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ſuper eadem baſi A B in-
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ter ſe ęqualia, quare O H
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æquidiſtabit A B, ideo-
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que vt D O ad O A, vel
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D B ad B M, ita D H ad
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H B, vel D A ad A I.
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<
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portionaliter ſectæ in B,
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A, quibus additæ ſunt D
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E, D G, æquales ipſis D
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B, D A, vtraq; </
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ſuntq; </
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la D M A, D I L ſimilia
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inter ſe, quare recta ngu-
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lum E M B ad quadratũ
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M A, ſiue E B ad B
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conic.</
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eſt vt rectãgulum G
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ad quadratum I L, cumque ſit I L minor I B, erit quadratum I L minus
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quadrato I B, ideoque rectangulum G I A ad quadratum I L, hoc eſt tranſ-
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uerſum E B ad rectum B F, habebit maiorem rationem, quàm rectangu-
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lum G I A ad quadratum I B, vel quàm tranſuerſum G A ad rectum A K;</
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mi conic.</
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ergo prima E B, ad ſecundam B F, maiorem habet rationem quàm tertia G
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A ad quartam A K, ſed eſt prima E B minor tertia G A, ergo, & </
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da B F erit minor quarta A K; </
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teribus: </
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">quare B F, rectum axis tranſuerſi, eſt _MINIMVM_, & </
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">cum demonſtratum ſit re-
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ctangulum G I A ad quadratum I L eſſe vt tranſuerſus axis E B ad rectum
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B F; </
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E B æquatur B F, rectangulum etiam D M H æquatur quadrato M A, &</
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conic.</
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tunc angulus D A M, ęqualis eſt angulo A H M, ergo etiam angulus D L
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æquabitur angulo I B L, hoc eſt linea I B æqualis erit I L, ſed erat rectan-
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gulum G I A æquale quadrato I L, ergo idem rectangulum G I A æqua-
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bitur quadrato I B, ſiue tranſuerſa diameter A G, eius recto A K æqualis
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erit, & </
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<
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">Cum ergo Hyperbole fuerit rectangula æquilatera, ad aliam quoque
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diametri applicationem æquilatera erit, ſed axis eſt tranſuerſorum
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_MIMVS_: </
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">ergo in Hyperbola, cuius axis tranſuerſus eius rectum adæquet,
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rectum axis aliorum rectorum eſt _MINIMVM_. </
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