Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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homologas ſimilium figurarum, BG, Zl, quarum & </
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<
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tangentium, BE, DG, Z &</
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<
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xml:space
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">, fl, incidentes ſunt ipſæ, BD, Zf,
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hæc autem etiam in cęteris traiectis planis, vt dictum eſt contingere
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oſtendemus, ergo, BG, Zl, EDG, & </
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<
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xml:space
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ſimilium cylindricorum, ſeu conicorum iam dictorum, & </
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<
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xml:space
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<
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rum tangentium planorum, AE, LG, K &</
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<
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xml:space
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">, XL, ergo in his ſoli-
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dis adſunt omnes conditiones defin. </
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<
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<
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xml:space
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">vt recolenti eafdem patefiet,
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igitur erunt iuxta eandem pariter ſimilia. </
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<
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xml:space
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">Aduerte autem, quod ſup-
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poſui planum, NG, tangere tam cylindricum, quam conicum, vt
<
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etiam, Vl, ne figura nimis confunderetur, & </
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<
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xml:space
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">vt fierent latera, E
<
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G, & </
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<
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xml:space
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">l, communia parallelogrammis, BG, Zl, & </
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<
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xml:space
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">triangulis, D
<
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EG, f & </
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<
s
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">l, valebit tamen eadem demonſtratio etiamſi plana ducta
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per, HG, Yl, tangentia cylindricos, diuerſa ſint à planis per eaſdem,
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HG, Yl, tranſeuntibus, ac tangentibus ipſos conicos, fient enim
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ſemper ſimilia triangula, EDG, & </
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ribus, EG, & </
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<
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xml:space
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">l, vt conſideranti facilè patebit, hæc autem nobis o-
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ſtendenda erant.</
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head
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eo figura erit, quæ per reuolutionem ipſum genuit.</
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note
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hoc autem plano per axem, AM, ducto ſecetur, quod in eo produ-
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cat figuram, ACDFG. </
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eſſe eam, quæ per reuolutionem ip-
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ſum ſolidum genuit. </
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uolui circa, AM, figura, quę dictum
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ſolidum genuit, donec reperiatur po-
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ſita in plano figuræ, ACDFG, igi-
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tur vel harum figurarum perimetri
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congruunt, vel non, ſi ſic ex illis fa-
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cta erit vna figura, ea nempè, quæ
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per reuolutionem generat dictum ſo-
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lidum, ſi verò non congruant, ali-
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quis punctus alterius ambituum di-
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ctarum figurarum non reperietur in
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reliquæ ambitu, ſit is punctus, B, qui
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reperiatur in ambitu figuræ, quæ per reuolutionem dictum ſolidum
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deſcripſit, quæ ſit ipſa, ABDFG, & </
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FG, cuius ambitus eſt communis ſectio plani ducti per axem, & </
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