Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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circa minorem axim BR, in
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0168-01
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qua prædictæ contingentibus
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perpendiculares ipſi BR occur-
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runt: </
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<
s
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xml:space
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">dico AC, quæ à remotiori
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contactu educitur minorem eſſe
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DG, quæ à propinquiori. </
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<
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cum ſit DO ad DG, vt I L ad IG,
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vel vt tranſuerſum latus ad
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">3. Co-
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roll. 90. h.</
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ctum, vel vt HL ad HC, vel vt
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AN ad AC, erit DO ad DG, vt
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AN ad AC, & </
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<
s
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">permutando, vt
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DO ad AN, ita DG ad AC, ſed
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eſt DO maior AN, vt ſupra ad numerum 5. </
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<
s
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xml:space
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">oſtenſum eſt, ergo, & </
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<
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erit ipſa AC. </
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<
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xml:space
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">Quod ſecundò oſtendere propoſitum fuit.</
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</
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">Dato angulo rectilineo, ad punctum in eius latere datum MA-
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XIMVM circulum inſcribere.</
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</
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<
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<
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">SIt datus angulus rectilineus ABC, & </
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">punctum in eius latere datum ſit A,
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ad quod oporteat _MAXIMVM_ circulum inſcribere.</
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</
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<
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<
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xml:space
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">Bifariam ſecetur angulus à recta BD, & </
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<
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">ex A ipſi AB perpendicularis eri-
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gatur AE, occurrens BD in E; </
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">& </
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<
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">centro E, interuallo EA deſcribatur circu-
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lus. </
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<
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xml:space
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">Dico hunc eſſe _MAXIMVM_ quæſitum.</
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</
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<
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<
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">Nam ſumpta BC ipſi BA æquali, iunctiſque AC, EC; </
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<
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">cum latera AB,
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BE, æqualia ſint lateribus CB, BE, & </
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<
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">anguli ad B æquales, erit EA æqualis
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EC. </
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<
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xml:space
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">Inſuper ſunt BA, AE, ipſis BC, CE æqualia, vtrunque vtrique, & </
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<
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xml:space
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">ba-
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ſis BE communis, ergo angulus BAE angulo BCE æqualis, nempe rectus
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quare circulus ex EA per C tranſibit, contigetque latera BA, BC, ſiue erit
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angulo ABC inſcriptus. </
s
>
<
s
xml:id
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xml:space
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">Dico hunc eſſe _MAXIMVM_ quæſitum.</
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<
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</
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<
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<
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xml:space
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">Nam ſi centra circulorum ad A pertinen-
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tium, fuerint in portione perpendicularis
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AE, inter A, & </
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<
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">ipſi, vt ſatis conſtat, erũt
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quidem angulo inſcripti, cum circulo quo-
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que inſcripti ſint; </
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<
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">ſed minores erunt circulo
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ADC cum ſint minoris radij; </
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<
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">illi verò quo-
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rum centra ſunt in producta AE, vt in F, ſunt
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quidem maiores, ſed latus BC omnino ſecát:
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</
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<
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">quoniam ducta F G parallela ad E C, quæ
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productæ A C occurrat in G, cum ſit AF ad
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FG, vt AE ad EC, ſitque AE ipſi EC æqua-
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lis, erit quoque AF æqualis FG: </
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<
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">quare cir-
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culus ex FA tranſibit per punctum G, quod
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eſt extra angulum; </
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<
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">ideoque in ſe remeans ſecabit omnino latus BC, quod
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eſt infinitæ extenſionis. </
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<
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