Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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mul adſcribi intelligatur, vel SECTIONES SIMVL ADSCRIPTÆ dican-
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tur, quando cum fuerint æqualiter inclinatæ earum diametri, & </
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<
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ductæ inter ſe mutuò congruant.</
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<
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xml:space
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ſectiones ABC, DEF æ-
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qualiter inclinatæ, ita di-
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ſpoſitę fuerint vt ipſarum
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diametri BG, EI ſibi mu-
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tuò congruant, & </
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vnius applicatę (quarum
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vna AG) congruant om-
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nibus alterius applicatis,
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(quarum vna ſit DI) ipſæ
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vocentur ſectiones ſimul
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adſcriptæ.</
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<
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">Coni-ſectio, vel circulus, coni-ſectioni, vel circulo inſcribi dicatur, vel
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SECTIO SECTIONI INSCRIPTA vocetur, quando cum fuerit altera al-
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teri adſcripta, ſit quoque tota intra eandem, nec alicubi ſe mutuò ſecent,
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licet in infinitum producantur, quæ in infinitum extendi poſſunt.</
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">Hoc eſt, ſi vt in prima, & </
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">ſecunda figura vtriuſque ordinis præcedentis
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ſchematis duæ coni-ſectiones ABC, DEF fuerint ſimul adſcriptæ, & </
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ipſarum vt DEF tota cadat intra aliam ABC, tunc dicatur ſectio DEF inſcri-
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pta ſectioni ABC.</
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gatur, vel SECTIO SECTIONI CIRCVMSCRIPTA dicatur, ſi cum fue-
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rit altera alteri adſcripta, tota quoque cadat extra eandem, nec alicubi ſe
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mutuò ſecent quamuis in infinitum abeant.</
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<
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">Qualis eſt in prædictis figuris ſectio ABC, quæ cum ſit adſcripta ſectioni
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DEF tota cadit extra eandem DEF.</
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punctum intra, aut extra ſectionem datum adſcribi, vel inſcribi, aut circum-
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ſcribi intelligatur, ſiue SECTIO SECTIONI PER VERTICEM, vel PER
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DATVM PVNCTVM INTRA, aut EXTRA SECTIONEM ADSCRI-
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PTA, vel INSCRIPTA, aut CIRCVMSCRIPTA dicatur, quando cum
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fuerit altera alteri adſcripta, vel inſcripta, aut circumſcripta, vnius diameter
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per datum punctum educta ſit quoque diameter alterius; </
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<
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">vt videre eſt in
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præcedentibus figuris.</
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fuerint ęqualiter inclinatę ipſarum latera ſint proportionalia, hoc eſt vt tran-
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ſuerſum vnius ad rectum, ita ſit tranſuerſum ad rectum alterius eiuſdem no-
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minis.</
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