Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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axis, MINIMVM verò rectum maioris.</
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<
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">ESto Ellipſis A B C D, cuius centrum E, axis minor A C, rectum A
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G, & </
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eſſe _MAXIMVM_; </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0223-01
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">Sit enim quælibet alia tranſuerſa diame-
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ter H I, cuius rectum H L, ſitque diame-
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ter M N ipſi H I coniugata, quæ media
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proportionalis erit inter I H, & </
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de quadratum ipſius M N æquabitur re-
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ctangulo I H L, vti etiam quadratum A C
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æquatur rectangulo D B F, & </
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B D rectangulo C A G; </
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">ſed eſt quadratum
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A C, minus quadrato M N, cum ſit tranſ-
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uerſa A C minor tranſuerſa M N,
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rectangulum D B F minus erit rectangulo
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I H L, quare B D ad H I minorem habe-
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bit rationem quàm H L ad B F, eſtque B
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D maior H I, ergo & </
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<
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">ibidem.</
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maior recto B F.</
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erit quadratum M N minus quadrato D B, ſiue rectangulum I H L minus
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rectangulo C A G, vnde I H ad C A minorem habebit rationem quàm
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A G ad H L, ſed eſt I H maior C A, ergo rectum A G erit maior
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">ibidem.</
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H L. </
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maior B F. </
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">Quare A G rectum minoris axis eſt _MAXIMVM_, B F verò
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maioris axis rectum, eſt _MINIMVM_. </
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">A puncto dato intra angulum rectilineum rectam applicare,
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cuius rectangulum ſegmentorum ſit MINIMVM.</
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<
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tet ex D rectam in angulo applicare, ita vt rectangulum ſub ipſius
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ſegmentis ſit _MINIMVM_.</
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dicularis applicetur A D C. </
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">Cum enim in triangulis B E A, B E C anguli ad E ſint recti, & </
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facti æquales, erunt reliqui anguli B A E, B C E æquales, & </
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C, baſim trianguli æquicruris A B C, pariter æquales.</
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