Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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omnes Ellipſis affectiones circulo communes eſſe, ſed ferè omnes etiam Hy-
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perbolæ, magnaque pars Parabolæ, præmittendo tamen nouas quaſdam ani-
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maduerſiones, cautioneſque perutiles, nemini, quod ſciam, adhuc cognitæs,
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præcipuèque vtendo methodo ab ipſo Apollonio ſatis diuerſa, certàque indu-
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ſtria propoſitionum figuris characteres diſponendo, ad hoc vt eadem demon-
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ſtratio cuin
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libet com-ſectioni ſimul inſeruiat, non abſimili modo ab eo, quo
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in ſuperiori Theoremate vſi ſumus, ex quibus maximum doctrinæ conicæ
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compendium oriretur; </
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">ſed quoniamid, plus laboris, ac temporis, quam in-
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genij requireret, libenter opusrelinquo ijs, quibus multum ocij ſuppetit,& </
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quos magis iuuat in alienas lucubrationes commentaria ſcribere, quàm vel
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ipſas latiùs promouere, vel nouas meditari, ac geometricè demonſtrare.</
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<
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">Quod autem in Apollonij ſubcontraria ſectione tranſuerſum, rectumque
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latus reperiatur eadem methodo, rationeque illorum rectangulorum qua vti-
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mur in præcedenti, quodque hæc ipſa latera inter ſe ſint æqualia manifeſtum
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fiet ex eo, quod mox demonſirabimus non tantum in prædicta ſectione ſub-
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contraria, quæ recta eſt plano trianguli per axem recto plano baſis coni ſcale-
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ni, ſed etiam ei quæ ſecat planum baſis com ſecundum rectam lineam perpen-
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dicularem baſi cuiuſcunq; </
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">trianguli per axem non iſoſcelis, vel ei, quæ ipſi baſi
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indirectum producitur, dummodò talis ſectio ex ipſomet triangulo, triangu-
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lum auferat ſibi ſimile, ſed ſubcontr ariè poſitum.</
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<
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">REpetitis igitur duabus vltimis præcedentibus figuris, intelligatur conũ
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ABC ſcalenum eſſe, ſectumque plano per axem, quodcunque trian-
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gulum efficiente ABC, dummodo non ſit æquicrure, (quod per doctrinam
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lib. </
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