Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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eorundem cubi ſunt æquales, ergo parabola, DAF, erit æqualis
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parabolæ, MHFC, quod oſtendere opuserat.</
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">_H_Inc patet, ſi diametri, AR, HO, vel axis, & </
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<
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">diameter ſint æquà-
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les, etiam, DF, XC, eſſe ęquales, nam oſtenſum eſt, QC, eſſe æqualem
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ipſi, RF, eſt autem, XC, dupla, CQ &</
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<
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">, DF, dupla, FR, ideò etiam,
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XC, DF, ſunt, æquales.</
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">EXpoſita ſemiparabola cum dimidia baſi, & </
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">axi, vel
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diametro totius, & </
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">completo parallelogrammo ſub
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dicto axi, vel diametro. </
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">& </
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<
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">ſemibaſi, deſcriptaque ellipſis
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quarta, vel circuli circa axem vel diametrum, & </
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baſim dictam, tanquam circa ſemiaxes, vel ſemidiame-
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tros coniugatas integræ ellipſis, vel circuli; </
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<
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matur vtcunque punctum in ſemibaſi, per quod ducatur
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recta linea ad oppoſitum latus parallelogrammi paralle-
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la dictæ axi, vel diametro, portio huius inter ſemibaſim,
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& </
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">curuam ellipſis, vel circuli incluſa, erit media propor-
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tionalis inter incluſam oppoſitis lateribus parallelogram-
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mi iam dicti, & </
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<
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">eadem ſemibaſi, ac curua parabolæ. </
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verò ſumatur punctum in axi, vel diametro iam dicta,
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& </
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<
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">per ipſum ducatur ſemibaſi parallela, producta vſq; </
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latus oppoſitum parallelogrammi iam dicti, & </
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extrema puncta curuæ parabolæ recta linea, huius portio
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incluſa inter axim, vel diametrum dictam, & </
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<
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rabolæ, erit media proportionalis inter eam, quæ inclu-
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ditur lateribus oppoſitis dicti parallelogrammi, & </
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quæ includitur lateribus trianguli ſub dicta axi, vel diame-
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tro, & </
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<
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219
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0327-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0327-01
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