Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
"/>
poſſemus habere, quot ſunt variationes inclinationum diametrorum
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ad baſes, quam tamen variationem per definitionem ſupradictam
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excludere neceſſarium eſſe exiſtimaui. </
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<
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xml:space
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definitioni hoc adiungatur, dico eam cum mea concordare, ſi pro
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ipſis ſectionibus tanquam figuris in-
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telligatur. </
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<
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xml:space
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">Ductis enim per vertices,
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A, R, baſibus, DF, QK, paralle-
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lis, illæ tangent dictas portiones, & </
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inter eaſdem ductas habebimus ip-
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ſas, AE, RG, illis ad eundem an-
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gulum incidentes ex eadem parte,
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quibus ſimiliter ad eandem partem
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diuiſis, vt in punctis, N, O; </
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</
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xml:space
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">& </
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<
s
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xml:space
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">per eadem ductis ipſis tangenti-
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bus parallelis, BM, CH, SP, TL,
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inuenimus eas, quęinter ipſas, AE,
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RG, & </
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<
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xml:space
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">circuitum figurarum, ADF, RQK, ad eandem partem
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continentur, & </
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<
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xml:space
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">diuidunt ipſas ſimiliter ad eandem partem, eodem
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ordine ſumptas, eſſe in proportione ipſarum, AE, RG, nam quia,
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DF, ad, EA, eſt vt, QK, ad, GR, permutando, DF, ad, QK,
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erit vt, EA, ad, GR, & </
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<
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">quia ipſæ, AE, RG, ſunt diametri, ad
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quas ordinatim applicantur dictæ parallelę, ideò ab eiſdem bifariam
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diuidentur, ergo, &</
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">, EF, ad, GK, erit vt, E
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A, ad GR, eodem modo oſtendemus tum, CO, ad, TX, tum, O
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H, ad, XL, eſſe vt, OA, ad, XR .</
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N, ad, SV, &</
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ad, GR, ſunt igitur figurę, ADF, RQK, ſimiles iuxta meam de-
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finitionem, earum verò, & </
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ex vna parte ſuntipſæ, DF, QK,) incidentes ſunt ipſæ, AE, RG.</
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<
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">_A_Ffert Commandinus ali@m definitionem ſimilium hyperbolarum,
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ſcilicet ſimiles eſſe, quarum coniuncta diametri inter ſe, vel qua-
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rum figuræ latera eandem proportionem babent, quam Dauid Riualtus
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in Com. </
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<
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dit concordare cum ſupradicta Apollonij, quam videat, qui voluerit:
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bit (ſumpta tamen hyp@rbola tanquam figura) vnde hac quoque hypo-
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teſi ſi opus fuerit, pariter vtemur ad paſſiones inde dependentes demon-
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ſtranda
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s.</
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