Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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dem altitudinem habentis.</
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">REpetito præcedenti diagrammate, dico Parabolen AB8 ſeſquitertiam
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eſſe inſcripti trianguli AB8.</
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">Nam ducta G9 parallela ad AC deſcribatur ſemi Parabole 9, 8, cuius dia-
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meter ſit 9C, & </
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AGC. </
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">Et cum ſit ſemi-Parabole ABC æqualis ſemi-Parabolæ CB8, &</
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prop. 14. h.</
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Parabole AGC æqualis ſemi-Parabolæ C98, ſitque C98 dimidium
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prop. 14. h.</
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(nam eſt C9 dimidium CB &</
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læ ABC, ſiue æqualis trilineo AHBCGA, ac etiam trilineo AEBH; </
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totum triangulum AEC ſeſqui alterum erit ſemi-Parabolæ ABC, ſiuc erit
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vt 6 ad 4, ſed ad triangulum ABC eſt vt 6 ad 3, cum ſit EC dupla CB, vnde
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ſemi-Parabole ABC ad triangulum ABC, hoc eſt dupla ad duplum, nempe
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Parabole AB8 ad inſcriptum triangulum AB8, erit vt 4 ad 3. </
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ſtrare oportebat.</
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">VT hoc loco, ex aduerſo indirectæ Antiquorum viæ per duplicem
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poſitionem, luce clarius pateat quantum facilitatis, breuitatis,
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atquæ euidentiæ naſciſcatur è noua, directaque methodo (rectè
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tamen cautèque vſurpata) acutiſsimi Geometræ Caualerij,
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per indiuiſibilium doctrinam, nobis amiciſsimam, ex hac alteram accipe
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eiuſdem theorematis demonſtr ationem, conſimili arte cōp@catam, ac in præ-
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cedenti.</
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dem altitudinem habentis.</
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tiam eſſe inſcripti trianguli ABC.</
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<
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F, FH parallela ad AD, ac deſcriptis, vt in præcedenti figura Parabola
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AED, & </
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ta ſit DC ducatur in tota ABC quælibet applicata NI. </
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M, eritque NM æqualis ML, & </
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">ſic de quibuslibet alijs applicatis ipſi AC æ-
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quidiſtantibus, quare omnes ſimul in portione ABD, omnibus ſimul in por-
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tione DBC æquales erunt, ſiue portio ABD æqualis DBC, nempè vtraque
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erit ſemi-Parabole, & </
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<
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">eadem ratione oſtendetur DHC ſemi-Parabolen eſſe.</
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