Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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erunt ſimiles, at ſunt per verticem E ſimul adſcriptæ, vnde PEQ minorum
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laterum inſcripta erit Hyperbolæ DEF maiorum laterum: </
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applicata quacunque TVP; </
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">cum Hyperbolæ ABC, PEQ ſint congruentes,
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& </
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<
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pta TP: </
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<
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cem ſimul adſcriptæ erit intercepta DX minor intercepta VP, vnde
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intercepta AD omnino erit maior reliqua intercepta TV; </
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<
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</
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<
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">quare huiuſmodi Hyperbolæ ABC, DEF ſunt ad ſe propiùs accedentes. </
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Quod erat ſecundò, &</
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">Tandem, bifariam ſectis tranſuerſis lateribus GB, GE, RE, in Y, Z, K,
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erit Y centrum Hyperbolæ ABC, Z verò centrum DEF, ac demum K cen-
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trum PEQ: </
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">cum ſit GB minor GE, erit dimidium GY minus dimidio GZ;
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">quare punctũ Z cadit infra Y: </
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dimidio EK, vnde K punctum cadit infra Z. </
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tris Y, Z, ducantur earum aſymptoti Y 2, Z 3, K 4, erit Z 3, parallela
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41. huius.</
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K 4, & </
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">quare aſymptoti omnes Y 2, Z 3,
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44. h.</
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erunt inter ſe parallelæ: </
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gulum ab aſymptotis comprehenſum, ipſa ſectionem ABC ſecabit, vt in
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11. h.</
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per quod ordinatim ducta recta 2 3 4, alias aſymptotos ſecantin 2 4, infra
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ipſam applicetur quælibet alia TVP, ſingulas Hyperbolas ſecans in T, V, P.
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<
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">Erit intercepta TP maior ſemper interuallo 2 4, ſed ablata intercepta
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eſt ſemper minor ablato interuallo 3 4, vnde reliqua intercepta TV
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datas ſectiones A B C, D E F, erit omnino maior reliquo interuallo 2 3,
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quod inter datarum ſectionum parallelas aſymptotos eſt interceptum, ac
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iuxta ordinatim ductis æquidiſtantes metitur. </
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ſtrandum.</
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