Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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eſt, inſcriptam, vel minorem eſſe ea, cuius tranſuerſum minus eſt; </
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<
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<
s
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xml:space
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tra eam eſſe circumſcriptam, ſiue maiorem, cuius tranſuerſum minus eſt.
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<
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<
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xml:space
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">figura, in qua ſectiones ſunt Hyperbolæ ſimul adſcriptæ cum eo-
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dem recto latere, oſtenſum fuit Hyperbolen DBE, cuius tranſuerſum BI ma-
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ius eſt, totam cadere intra Hyperbolen ABC, cuius tranſuerſum BL minus
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eſt, & </
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<
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">ideo DBE erit inſcripta, ſiue minor; </
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<
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<
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xml:space
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">è contra ipſa ABC, cuius tranſ-
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uerſum eſt minus, erit circumſcripta, ſiue maior.</
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<
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<
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verticé ſimul adſcriptis cũ eodem recto latere, eam eſſe inſcriptam, ſiue
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minorem, cuius tranſuerſum latus minus eſt, & </
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<
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vel maiorem eſſe, cuius tranſuerſum maius eſt: </
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ra oſtenſum fuit Ellipſim, vel circulum DBE, cuius tranſuerſum BI minus
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eſt, totam cadere intra Ellipſim, vel circulum ABC, cuius latus tranſuerſum
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BL maius eſt; </
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<
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xml:space
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">quare ipſa DBE erit inſcripta, ſiue minor: </
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<
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vel circulus ABC erit circumſcriptus, ſiue maior, &</
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<
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xml:space
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">MAnifeſtum eſt etiam ſimiles coni-ſectiones per vertices ſimul adſcri-
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ptas habere regulas parallelas, & </
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<
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">eam ſectionem eſſe inſcriptam, vel
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minorem, cuius latera minora ſunt; </
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<
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xml:space
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maiorem, cuius latera ſunt maiora. </
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<
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<
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xml:space
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">figura coni-ſectio-
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nes ABC, DBE eiuſdem nominis, ac per verticem B ſimul adſcriptæ, fuerint
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ſimiles, erit tranſuerſum LB ad rectum BH vt tranſuerſum IB ad rectum BG,
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& </
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">diuidendo, LI ad IB, vt HG ad GB, vndæ regulæ LH,
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IG erunt parallelæ, ſed in hoc Theoremate demonſtratum eſt ſectioné ABE
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minorum laterum, totam cadere intra ſectionem ABC maiorum laterum,
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ergo ipſa DBE erit inſcripta; </
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<
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">è contra demonſtrauimus ABC maiorum
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laterum totam cadere extra DBE minorum laterum, ac propterea erit ei cir-
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cumſcripta.</
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<
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ni-ſectionibus per vertices ſimul adſcriptis, quadrata ſemi- applicata-
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rum ex eodem diametri puncto inter ſe ſunt vt earundem latitudines. </
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dimus enim in qualibet præcedentis ſchematis figura, quadratum ſemi-ap-
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plicatæ MF, in ſectione ABC, ad quadratum ſemi-applicatæ NF, in ſectio-
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ne DBE, eſſe vt latitudo propria FP, ad propriam latitudinem FO.</
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