Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Erigatur ex A contingenti A G perpendicularis A L, quæ axi
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mi huius.</
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ret in L, cui applicata A H, erit intercepta L H æqualis dimidio
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mi huius.</
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B I, hoc eſt dupla interuallo D B, (cum punctum D diſtet à vertice B
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per quartam recti lateris partem ex hypoteſi) & </
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mi conic.</
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G B, quare, & </
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">tota L G dupla eſt tota G D, ſiue L D æqualis D G, eſt-
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que angulus L A G rectus, quare ſi
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cum centro D, interuallo G, vel L
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circulus deſcribatur, ipſe omnino
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tranſibit per A; </
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<
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">vnde D A item æ-
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qualis erit ipſis D G, D L, ſiue L G
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erit dupla D A. </
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<
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">Et cum rectum axis
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B D, ad rectum diametri A E, ſit vt
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quadratum A H ad A G, vel
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24. huius.</
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triangulorum ſimilitudinem, vt qua-
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dratum A L ad L G, vel vt recta
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H L ad rectam L G (cum L A ſit
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media proportionalis inter G L, L H)
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ſumptis harum ſubduplis, erit rectũ
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axis ad rectum diametri A E, vt D
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B dimidium H L ad D A dimidium L G. </
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<
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ri quartæ parti rectorum, earum diametrorum, quarum vertices
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ſint termini, quibus ipſæ eductæ ſectioni occurrunt: </
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<
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B D ad rectum diametri A E, eſt vt D B ad D A, eſtque D B quarta pars
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recti B I, quare, & </
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<
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">D A erit quarta pars recti lateris diametri A E, & </
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">D F
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quadrans recti, diametri F R. </
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<
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">Vnde quò diametri ab axe remotiores
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fuerint, eò ipſarum recta maiora erunt. </
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<
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">PAtet etiam, quamlibet eductam ex foco, ęquari aggregato ex inter-
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uallo foci ab axis vertice, & </
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plicatam ex occurſu eductæ cum ſectione. </
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<
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">Oſtenſa eſt enim D A æqua-
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lis D G, quæ æqualis eſt aggregato G B, cum B D, vel H B cum B D.</
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vel parallelarum externus E A M, æqualis angulo D A G, ſed M
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A G Parabolen contingit in A, quare ex Opticæ legibus, ſi E A fuerit
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radius incidens ad concauam peripheriam A B C, ipſe A D erit
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& clariùs
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quàm à
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Vitellione
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in 41. 9.</
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xus, atque omnes radij axi Parabolę æquidiſtantes in punctum D coi-
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bunt; </
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