Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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<
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ipſum non immoror.</
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">SI ad baſim datæ parabolæ ordinatim applicentur vtcun-
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que rectæ lineæ, triangula ſub ipſis, & </
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<
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">portionibus baſis
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abijſdem abſciſſis, erunt vt parallelepipeda ſub baſibus qua-
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dratis abſciſſarum à baſi, altitudinibus autem reſiduis ipſius
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baſis demptis abſciſſis.</
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<
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">Sit parabola, HGA, cuius baſis, HA, axis, vel diameter, GO,
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ſint autem ductæ duæ vtcunq; </
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">ordinatim applicatæ adipſam baſim,
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HA, ipſæ, ST, VX, & </
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<
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">iungantur, SH, VH. </
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">Dico triangulum,
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VHX, ad triangulum, HST, eſſe vt parallelepipedum ſub altitudi-
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ne, AX, baſi quadrato, XH, ad parallelepipedum ſub altitudine, A
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T, baſi quadrato, TH. </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0317-01
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vni angulo æqualem habentia ratio-
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nem habent ex ratione laterum illis
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angulis circumſtãtium compoſitam,
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ideò triangulum, VHX, ad triangu-
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lum, SHT, habebit rationem com-
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poſitam ex ea, quam habet, VX, ad,
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ST, ideſt rectangulum, AXH, ad
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4. Gen. 34,
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lib. 2.</
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rectangulum, ATH, & </
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habet, XH, ad, HT, ſed iſtæ duæ
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rationes componunt rationem paral-
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lelepipedi ſub altitudine, HX, baſi
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rectangulo, AXH, ad parallelepi-
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pedum ſub altitudine, HT, baſi re-
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ctangulo, HTA, . </
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ſub altitudine, AX, baſi quadrato, XH, ad parallelepipedum ſub
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altitudine, AT, baſi quadrato, TH, ergo triangulum, VHX, ad
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triangulum, SHT, erit vt parallelepipedum ſub altitudine, AX, baſi
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quadrato, XH, ad parallelepipedum ſub altitudine, AT, baſi qua-
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drato, TH, quod erat oſtendendum.</
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