Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
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191 - 200
201 - 210
211 - 220
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bus ſe contingunt; </
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<
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<
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xml:space
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">in duobus tantùm punctis ſe mutuò ſecant. </
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<
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dem erat demonſtrandum.</
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<
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xml:space
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">PAtet hinc, quod ſi regulæ coni-ſectionum per vertices ſimul adſcripta-
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rum ſibi ipſis congruant ſectiones quoque erunt inter ſe congruentes,
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vt in primis quatuor figuris præcedentis ſchematis oſtenſum eſt; </
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<
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xml:space
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<
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xml:space
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">ſi fuerint
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inter ſe congruentes, etiam ipſarum regulæ ſimul congruent: </
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<
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læ ſimul congruunt, congruunt quoque, & </
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<
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">latera, & </
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">è conuerſo, cum ad æ-
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quales angulos inter ſe diſpoſita intelligantur, quare cum latera fuerint inter
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ſe congruentia ſiue æqualia, ſectiones quoque inter ſe congruentes erunt; </
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ſi ſectiones fuerint congruentes etiam ipſarum latera æqualia erunt.</
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<
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<
s
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xml:space
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">Si verò regulę infra recta ſectionum latera ex vertice contingenter appli-
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cata diſiunctim procedentes nunquam ſimul conueniant, nec ipſæ ſectiones
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vnquam conuenient, ſed in vertice ſe mutuò contingent, & </
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<
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xml:space
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">ea inſcripta erit,
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ſiue minor, cuius regula infra prædictam contingentem diametro ſectionum
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ſit propior, ſeu cadat tota inter diametrum, & </
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<
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</
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<
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">quæ è contra circumſcripta erit, ſiue maior, vt apparet in 26. </
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<
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xml:space
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quentibus.</
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<
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xml:space
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">Si tandem ipſarum regulæ infra contingentes ex vertice ſe mutuò ſecent,
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ſectiones quoque, ſed in duobus tantùm punctis hinc inde à vertice (in quo
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ſe tangunt) ſe mutuò ſecabunt, in illis nempe, quæ ſunt extrema eiuſdem
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ordinatim applicatæ, ex regularum interſectione eductæ, ſuper qua duæ co-
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ni-ſectionum portiones inerunt, quarum ea erit inſcripta, cuius regulæ ſe-
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gmentum inter prædictam applicatam, & </
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<
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pinquius ſit diametro ſectionum, altera verò circumſcripta, ſiue maior cuius
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regulæ ſegmentum à prædicta diametro magis diſtet, quod omne ſatis patet
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ex reliquis eiuſdem ſchcmatis figuris.</
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xml:space
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">COROLL. II.</
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<
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">in alijs coni-ſectionibus eiuſdem nominis
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per vertices ſimul adſcriptis, cum eodem tranſuerſo latere, illam, quę
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minus habet rectum latus inſcriptam, ſiue minorem eſſe ea cuius rectum la-
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tus maius eſt, & </
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<
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<
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<
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ſunt eiuſdem nominis, vti etiam in 15. </
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<
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">(diximus enim circulum non
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incongruè haberi poſſe pro Ellipſi) demonſtratum eſt ſectionem DBE, cuius
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rectum BG minus eſt recto BH ſectionis ABC, totam cadere intra ABC, vn-
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de erit inſcripta, ſiue minor, & </
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eſt totam cadere extra DBE, cuius rectum eſt minus: </
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<
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cumſcripta, ſiue maior.</
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<
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cum æqualibus rectis lateribus, illam, cuius tranſuerſum latus </
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