Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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I D, I E, I F, I G ex aſſumpto puncto I ad datarum terminos B, C, D, E,
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F, G; </
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">itaque aggregatum ductarum ex A æquales angulos inter ſe efficien-
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tes, & </
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">quatuor rectos ſimul complentes eſt _MINIMVM_. </
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<
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<
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">ſuper latera B A, B C deſcribantur ad partes baſis A C ſimiles
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circuli portiones A E B, C D B capientes angulos graduum 120. </
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Dico ipſarum peripherias ſe mutuò ſecare, atque omnino intra
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triangulum A B C.</
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harum portionum peripheriam contingente, ipſa, & </
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continget: </
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lis erit ei, qui ſit in alterna portione A E B, nempe erit gr. </
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rationem angulus G B C erit grad. </
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rectis, erit pariter gr. </
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gulum ad partes G, vt in G: </
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ducta G B, eſſet angulus G B A mi-
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noreo, qui fit à contingente ex B cũ
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ſecante B A, ſiue minor facto in al-
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terna portione A E B, qui eſt grad.
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</
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120. </
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360. </
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item eſt contra hypotheſim, cum ſit
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minor; </
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pherias ſe mutuò ſecare infra B ad
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partes baſis A C neceſſe eſt.</
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">Verùm ipſarum interſectio haud fiet in baſi A C, nec infra, quoniam
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ſi in ipſa baſi A C, vt in F, eſſet, ex conſtructione, angulus A F B grad.
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B, C F B eſſent duobus rectis maiores; </
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ctos adæquent.</
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<
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">Sitandem eædem peripheriæ ſe mutuò ſecarent infra baſim A C, vt in H;
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">iunctis A H, C H, eſſent pariter, ex conſtructione, duo ſimul anguli A H B,
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C H B, ſiue vnicus A H C maior duobus rectis; </
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duobus rectis deficiat per aggregatum duorum angulorum A C H, C A H. </
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Quamobrem huiuſmodi ſimilium portionum peripherię neceſſariò ſe mutuò
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ſecabunt, atque intra triangulum A B C|. </
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