Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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tra ſectionem, à quo ductæ ſunt Q M, Q E aſymptotis parallelæ, & </
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perbolæ occurrentes in M, E, & </
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">ab altero occurſuum E, ducta eſt E G H,
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ſecans Hyperbolen in G, & </
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<
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">aſymptoton H L in H, erunt iunctæ H Q,
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M G O inter ſe parallelæ; </
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<
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xml:space
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">quare in triangulo Q E H, recta G M,
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baſi H Q æquidiſtat, producta conueniet cum latere E Q, vt in O; </
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<
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que E Q ad Q O, vt E H ad H G, hoc eſt vt tranſuerſum A B ad rectum
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B F, ſed E Q ad Q O, ſumpta communi altitudine Q P, eſt vt rectangu-
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lum E Q P ad rectangulum O Q P, ergo rectangulum E Q P ad O Q P erit
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vt tranſuerſum ad rectum, vel vt idem rectangulum E Q P ad
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conic.</
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tum Q M; </
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<
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">vnde rectangulum O Q P, æquale eſt quadrato Q M, eſtque
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QM ipſi O P perpendicularis, ergo angulus O M P rectus eſt, & </
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<
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pt. Pappi.</
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ptima figura, qui ei deinceps eſt G M P rectus erit, ſed eſt G M extra
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ſectionem, contingenti M P perpendicularis: </
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<
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">quare G M erit _MINIMA_.</
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At, in octaua figura, M P Ellipſim contingit, & </
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eſt intra Ellipſim, ſed non excedit interceptam M O inter contactum, & </
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maiorem axim, quare G M erit _MINIMA_.</
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num. 1.</
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">Quod tandem in quouis prædictorum ſchematum, ducta G N ſit _MA-_
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_XIMA_, ita oſtendetur, ſed in nona tantùm figura, ne in reliquis noua li-
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nearum, & </
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<
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">Secet ergo G N ſemi-axim minorem A E in K, & </
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applicetur N S, contingens agatur N T, iungaturque S H.</
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</
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<
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<
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">Et cum à puncto S, & </
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">in angulo aſymptotali H L I intra ſectionem
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ductæ ſint S E, S N aſymptotis parallelæ, Hyperbolæ occurrentes in E,
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N, & </
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<
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">ab altero occurſuum E ducta ſit E G H, Hyperbolen ſecans in G,
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& </
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<
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">aſymptoton in H, erunt iunctæ S H, N R G inter ſe parallelæ
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in triangulo H E S, erit E S ad S R, vt E H ad H G, vel vt tranſuerſum
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D B ad rectum B F, vel vt rectangulum E S T ad quadratum S N,
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conic.</
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E S ad S R, eſt vt idem rectangulum E S T ad rectangulum R S T, ergo
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quadratum S N æquale eſt rectangulo R S T, ex quo angulus R N T re-
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ctus erit, ſed T N Ellipſim contingit in N, eſtque N G maior intercepta
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N K inter contactum, & </
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<
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">minorem axim, quare G N omnino erit
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num. 2.</
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_MA_ quæſita. </
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<
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">DE inuentione MAXIMARVM à puncto dato ad univerſam
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Parabolæ, vel Hyperbolæ peripheriam hactenus w
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ihil egimus,
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cum manifeſtè pateat ad eas educi minimè poſſe lineas tantæ
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longitudinis, quin ipſis maiores, & </
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<
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tum reperiantur; </
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<
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">eò quod ſectiones ipſæ ſint infinitæ extenſionis: </
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ſultò de hac re demonſtrationem omiſimus, cum hæc in promptu ſatis ſit.
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</
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<
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">Verùm ſi quærantur MAXIMAE, ducibiles à puncto extra ſectionem da-
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to, ad conuexas tantùm quarumlibet coni-ſectionum peripherias: </
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<
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fuerit in axe producto, ex eo ductæ lineæ contingentes æquales erunt, & </
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XIMAE ad ipſius ſectionis conuexam peripheriam. </
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<
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rit extra axim Parabolæ vel Hyperbolæ, ſed intra angulum ab </
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