Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VI.
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">DAto cylindro tympanum ſphærale eidem æquale cõ-
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ſtituere, cuius axis ſemidiametro baſis ſit æqualis.</
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<
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">Sit datus cylindrus,
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fig-0493-01
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fig-0493-01a
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333
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0493-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0493-01
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ABC, cuius axis, AD,
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baſis, BC, oportet illi
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æquale tympanu ſphę-
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rale conſtituere, cuius
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axis ſemidiametro ba-
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ſis ſit æqualis. </
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fiat exponatur recta li-
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nea terminata quæcũ-
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que, EI, quæ ſit bifariã
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ſecta in, G, & </
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<
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</
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">circulo cuicunq; </
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ſcriptum ad eundem
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circulum, ita fiat, GE,
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ad, EF, ſumatur dein-
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de, FH, quæ ſit exceſ-
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ſus, quo, FE, ſuperat
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{2/3}. </
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<
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">tertiæ proportiona-
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lis duarum, IE, EG,
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deinde vt, HI, ad, IE, ita fiat, AD, ad, LO, altitudinem alterius
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cylindri in baſi, NP, æquali ipſi, BC, exiſtentis, & </
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<
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">tandem inter
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LO, &</
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<
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">, ON, baſis ſemidiametrum, ſumantur duæ mediæ conti-
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nuò proportionales, QO, OR, & </
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<
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">in altitudine æquali, OR, nem-
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pè, T8, baſi, ℟8, æquali eidem, OR, fiat parallelogrammum re-
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ctangulum, 58, in cuius plano deſcribatur ſemicirculus, SY℟, & </
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ipſum cum parallelogrammo reuo uatur circa manentem axim,
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T8, donec redeat vnde diſceſſit, patet autem, quod ex parallelo-
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grammo fiet cylindrus, vt, Sφ, & </
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<
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">ex figura, SY℟8T, tympanum
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ſphærale, 5Yφ. </
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">Dico igitur hoc tympanum eſſe æquale dato cy-
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lindro, ABC, &</
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<
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">, T8, æqualem ipſi, 8℟, ſemidiametro baſis, ℟φ. </
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Sint parallelogrammum, Sφ, & </
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<
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">figura, SYφ, per axem tranſeun-
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tia, & </
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<
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">, circulorum ducta, ſecans, T8, in, Z,
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manifeſtum eſt igitur, quod, XZ, bifariam ſecabitur à circumfe-
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rentia, SY℟, vt in, Y, cum, 8℟, ſit æqualis, ℟S, & </
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<
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autem ſit dupla, XY, vnde ſi ſecetur, ℟8, bifariam in, 4@erit, ℟4,
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æqualis ipſi, XY, ſit autem ab ea dempta, ℟@, ad qua ?</
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<
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