Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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& </
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">in reliquis, erunt proprijs ſemi- diametris proportionalia, hoc eſt ipſæ
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portiones æquales erunt. </
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<
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xml:space
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">De portionibus tandem eiuſdem anguli,
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">40. h.</
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ſunt triangula, iam notum eſt, quandò baſes ipſorum altitudinibus ſint reci-
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procè proportionales, ipſa triangula eſſe æqualia. </
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<
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dò probandum erat.</
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xml:space
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">Haud incongruum, neque inutile duximus hic adnotaſſe Theorema
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huiuſmodi.</
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">Æquales portiones eiuſdem coni-ſectionis, vel circuli (quæ
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tamen in Ellipſi ſint, vel vnà æquales, vel vnà maiores, vel vnà
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minores ſemi- Ellipſi) ad inſcripta ſibi triangula, (nempè ad ea,
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quorum baſes eædem ſunt, ac portionum, eædemque altitudi-
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nes, ſiuè ijdem vertices) vel ad circumſcripta parallelogram-
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ma, ſunt inter ſe in vnà eademque ratione.</
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<
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">NAm cum baſes æqualium portionum eiuſdem coni- ſectionis, vel cir-
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culi earum altitudinibus ſint reciprocæ, baſes quoque
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xml:space
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">65. h. ad
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num. 1.</
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triangulorum, eorum altitudinibus reciprocabuntur, cum vtrobique altitu-
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dines, & </
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<
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<
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">ac propterea ipſa triangula æqualia erunt.
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<
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">Quare, vt portio ad portionem, ita triangulum ad triangulum, ob æquali-
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tatem tùm portionum, tùm triangulorum; </
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<
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xml:space
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">permutando, portio ad ſibi in-
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ſcriptum triangulum, vt altera æqualis portio de eadem coni- ſectione, vel
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circulo ad ſibi inſcriptum triangulum. </
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<
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xml:space
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">Et ſumptis conſequentium duplis,
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portio ad circumſcriptum parallelogrammum, erit vt altera portio ad cir-
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cumſcriptum parallelogrammum. </
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<
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">c.</
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<
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xml:space
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">Hoc de ſolis Parabolæ portionibus, etiam ſi inæqualibus, nec de
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eadem Parabola, manifeſtum iam erat ex Archimede (omnis
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enim Parabolæ portio ad ſibi inſcriptum triangulum ha-
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bet rationem ſeſquitertiam.) </
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<
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coni- ſectionum æqualibus portionibus,
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non dum.</
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