Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
s
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xml:space
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">Iam ſi per verticem B ducatur in plano portionis E B G recta B L, ipſam
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xml:space
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mi conic.</
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portionem contingens, hæc baſi E G æquidiſtabit: </
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">& </
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<
s
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xml:space
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">ſi per B L concipia- tur planum duci, quod plano per axem E B G ſit erectum, id ſolidæ por-
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<
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symbol
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tionis ſuperficiem continget in B, atque baſi E H G I erit parallelum
<
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xml:space
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">per Sch.
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Clauijpoſt
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18. vndec.
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elem.</
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vtrunque planorum ſit eidem E B G rectum, & </
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<
s
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xml:space
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">communes ſectiones B L,
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E G ſint parallelæ. </
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<
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xml:space
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<
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</
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<
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<
s
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xml:space
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">Siverò planum ſecans E H G I rectum non fuerit ad axem B D; </
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<
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<
s
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ſectio erit Ellipſis) ſecetur denuò datum ſolidum quocunque alio plano
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15. Arch.
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de Conoi.
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&c.</
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H C I ad axem recto: </
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<
s
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xml:space
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">(quod tamen non tranſeat per interſectionem axis B
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D cum plano E H G I, ſi hoc axem ſecuerit intra ſolidum) id in ſolido ſe-
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ctionem faciet circulum, centrum habentem in axe B D, vti in D,
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xml:space
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">12. Arch.
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ib. à Co-
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mãd. reſt.</
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autem ſecabit baſim E H G I per communem rectam H I tùm in Ellipſi, tùm
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in circulo applicatam, cui ex D, circuli centro, ducta perpendiculari D M;
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</
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<
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xml:space
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">per axem B D, ac rectam D M agatur planum in ſolido efficiens genitricem
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ſectionem E A B G C, cuius communis ſectio cum circulo erit diameter A
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C, & </
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<
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<
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xml:space
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xlink:href
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nem hanc per B D axem du-
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ctam ad ſecans planum E H
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G I, ſiue ad baſim ſolidę por-
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tionis E F G rectam eſſe.
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</
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<
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xml:space
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">Quoniam cum planum circu-
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li E H C I rectum ſit ad pla-
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nũ per axem E A B C, cumq; </
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<
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linea I M in circulo perpen-
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dicularis ſit ad A C horum
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planorum communem ſectio-
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nem, erit eadem linea I M
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recta ad planum per
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xml:space
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vnd. Ele.</
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E A B C: </
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<
s
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">quare omnia plana, quæ per ipſam ducentur ad idem planum E A
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B C recta erunt, ſed E H G I baſis ſolidæ portionis tranſit per I M,
<
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Elem.</
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baſis E H G I, ſiue planum ſecans rectum erit ad planum per axem E A B C,
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ſiue id rectum ad planum ſecans, hoc eſt ad baſim ſolidæ portionis. </
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<
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primò, &</
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<
s
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xml:space
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">Cum ergo E G ſit communis ſectio planorum, eius ſcilicet, quod ſolidũ
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ſecat, & </
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<
s
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">cius, quod per axem ducitur erectum ſuper planum ſecans, ipſa E
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G erit axis Ellipſis E H G I, qua bifariam ſecta in N, erit N Ellipſis
<
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15. Arch.
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de Conoi.
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&c.</
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trum, ex quo, in plana portione E F G ſectionis per axem à recta E G ab-
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ſciſſæ, & </
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<
s
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">per F
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ſectionem contingente F O, per ipſam F O agatur planum, quod ad
<
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pr. h.</
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planum per axem E B G rectum ſit, id ſolidæ portionis E F G ſuperficiem
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<
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continget in F, & </
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<
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<
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<
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<
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Clauijpoſt
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18. vndec.
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Elem.</
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fuerit ergo Conoides quodcunque, vel Sphæra, &</
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<
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<
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<
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erat faciendum, ac demondrandum.</
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