Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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xml:space
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">_N_Eminem profectò mathamaticarum demon-
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ſtrationum dulceainem, vel primoribus la-
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bris vix attigiſſe puto, qui (non ſccus ac,
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mellis in arbore latentis deguſtata paululũ
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fuauitate, innumera licet ferientibus certa-
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tim aculeis apium caterua deglutientẽ Vr-
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ſum agrè arcere poſſunt) ſummarum, qua illas commitantur dif-
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ficult atum copia crebris velut ictibus obliſtenterepulſus, ad ſatie-
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catem vſq; </
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<
s
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">eadem vbiq; </
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s
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">perfundi totis viribus non contendat.
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</
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<
s
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xml:space
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">Talia tibi amice Lector, qui melleos hoſce fructus depaſcere con-
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ſueſti, cuiſdam in Geometriarei admiranda caſu in me orta ſpe-
<
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culationis occaſione, parta, huiuſce dulcedinis amore flagranti,
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libanda propone. </
s
>
<
s
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xml:space
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">Cum ergo ſolidorum, quæ ex reuolutione circa
<
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axim oriuntur, genefim aliquando meditarer, rationemq; </
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<
s
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<
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tium planarum figurarum cum genitis ſolidis compararem, maxi-
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mè ſanè admirabar quod à propriorum parẽtum conditione adeò
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natæ figuræ degenerarent, vt aliam omninò ab eiſdem rationem
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ſequi viderentur. </
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>
<
s
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xml:space
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">Cylindrus enim exempli gratia, in eadem ba-
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ſi, & </
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<
s
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">circa eundem axim, cum cono conſtitutus, eſt eiuſdem tri-
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<
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xml:space
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">_10. Duod._
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_Elem._</
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vlus, cum tamen ex parallelogrammo trianguli dictum conum
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xml:space
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">_41. Pri._
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_Elem._</
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generantis duplo per reuolutionem oriatur. </
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<
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">Similiter ſi in eadẽ
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baſi, & </
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<
s
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">circa eundem axim, bæmiſphærium, vel hamuphæroides,
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necnon conoides parabolicum, atq; </
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<
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">cylindcus, extiterint, hic erit
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hæmiſphery, vel hæmiſphæroidis ſexquialter, conoidis verò du-
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_34.l 3._</
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plus, cum tamen gignens par allelogrammum dictum cylindrum
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_51.l.4._</
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ad inſcriptum gignentem circulum, ſeu ellipſim, proximèrationẽ
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">_A ch._
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_de Dim._
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_Cuc._</
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habeat, quam quatuordecim, ad vndecim ad parabolã verò ſit in
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ratione ſexquialteræ. </
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>
<
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">Quinimmò & </
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>
<
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">in planis figuris per reuolu.
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</
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xml:space
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">_Piop. I._
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_l. 4._</
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tionẽ rectarum linearum circa punctum genitis, quales ſunt cir-
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culi, eandem varietatem licet experiri. </
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<
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concentrici intelligantur expoſiti radios habentes ex. </
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<
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<
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portione numcrorum ab vnitate deinceps expoſitorum, ipſi circuli
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non eandem radiorum proportionem conſeruabunt, ſedeam, </
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