Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBERI.
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<
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">Sint cylindrici quicunque, AH, KY; </
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<
s
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echoid-s1863
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">ſeu conici in ijſdem baſibus,
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& </
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<
s
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xml:space
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">altitudinibus (vt vna vice vtriuſq; </
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<
s
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echoid-s1865
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xml:space
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">demonſtrationem abſoluamus)
<
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NLH, VXY, ſimiles iuxta definit. </
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<
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<
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<
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xml:space
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">Dico eoſdem etiam
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eſſe ſimiles iuxta definit. </
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<
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<
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">Quoniam ergo vtraque prædicta ſolida
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">Defin. 7.</
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ſunt ſimilia, erunt baſes, LH, XY, ſimiles, ducantur earum oppo-
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ſitę tangentes, quę ſint homologarum regulę, ipſę, LD, HG, X f,
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">Coroll. 1.</
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0093-01
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Y l, quarum, & </
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<
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">B. Def. 10.</
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lium figurarum incidentes ſint ipſæ,
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DG, f l, quæ etiam pro regulis alia-
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23.</
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rum homologarum ſumi poterunt,
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ſint ergo duę quæcunque homologę
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parallelę incidentibus, D G, fl, ip-
<
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ſæ, LH, XY, ſi ergo per has, & </
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<
s
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echoid-s1872
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xml:space
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<
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xlink:label
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note-0093-05
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xml:space
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">Defin. 7.</
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tera cylindricorum, vel conicorum
<
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iam dictorum extendantur plana, ab
<
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ijs producentur in cylindricis ſimilia
<
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parallelogramma, & </
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<
s
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="
echoid-s1873
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">in conicis ſimi-
<
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lia triangula, quę etiam erunt ad ba-
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ſes æquè ad eandem partem inclina-
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ta. </
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>
<
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xml:space
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">Extendantur ergo per oppoſitas
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tangentes, LD, HG; </
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<
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xml:space
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">Xf, Yl, pla-
<
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na tangentia tam cylindricos, quam
<
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conicos iam dictos, & </
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<
s
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="
echoid-s1876
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xml:space
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">hęc ſimul cum
<
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planis baſium indefinitè producan-
<
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tur ad partes incidentium, DG, fl,
<
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& </
s
>
<
s
xml:id
="
echoid-s1877
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xml:space
="
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">tandem per, DG, fl, cum ſint
<
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parallelæ, extendantur plana ipſis,
<
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AH, KY, parallela ſecantia iam pro-
<
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ducta plana in rectis, DG, GE, E
<
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B, BD, DE, fl, l &</
s
>
<
s
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">, & </
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<
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">Z, Zf, f
<
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<
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note-0093-06
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note-0093-06a
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">Defin. 13.
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vndec. El.</
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&</
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<
s
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">, erunt ergo parallelepipeda, AG,
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Kl, & </
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<
s
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echoid-s1881
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xml:space
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">priſmata, LNGD, XVlf,
<
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<
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xml:space
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">24. Vnd.
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Elem.</
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ergo erit parallelogrammum, BG,
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ſimile ipſi, AH, &</
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<
s
xml:id
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echoid-s1882
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xml:space
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">, Zl, ſimile, K
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Y, quæ cum ſint inter ſe ſimilia, e-
<
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tiam, BG, Zl, erunt ſimilia, ſic e-
<
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tiam oſtendemus triangula, EDG,
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& </
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>
<
s
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echoid-s1883
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xml:space
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">fl, eſſe ſimilia, ſub intellige iuxta
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definitionem Euclidis, ergo erunt e-
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tiam ſimilia iuxta defin. </
s
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<
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">10. </
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<
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">Ducantur duo plana oppoſitis tangenti-
<
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<
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">27. huius.</
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bus intermedia, ac parallela, altitudines dictorum ſolidorum reipectu
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baſium, LH, XY, ſumptas, ſimiliter ad eandem partem </
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