Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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logrammo, FP, quod dicimus ſimilare, ſemper eſſe cylindricum, geni-
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tum verò ex triangulo, DEP, ſemper eſſe conicum, vt etiam accidit in
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omni parallelogrammo, & </
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<
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">triangulo, dummodò regula ſit vnum laterum
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eorundem, ſolida igitur ſimilariagenita ex parallelogrammis ſunt cy-
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lindrici, genita verò ex triangulis ſunt conici, genita inquam, regula,
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vno laterum eorundem exiſtente; </
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<
s
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xml:space
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">quod ſi figuræ quæ dicuntur omnes fi-
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guræ ſimiles par allelogrammidati, regula vno laterum, ſint eirculi, ille
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cylindricus erit cylindrus; </
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<
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xml:space
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">& </
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<
s
xml:id
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echoid-s6458
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xml:space
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">ſi, quæ dicuntur omnes figuræ ſimiles dati
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trianguli ſint pariter cirouli, regula vno laterum, conicus erit conus;
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</
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<
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xml:space
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">nomine ergo communi bic cylindrus, & </
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<
s
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echoid-s6460
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xml:space
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">conus dicti ſunt ſolida ſimila-
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ria nomine particulari dicti ſunt cylindricus, & </
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<
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">conicus, ſed nomine,
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magis particulari, & </
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<
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">proprio dicuntur cylindrus, & </
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<
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">_34. Lib. 2._</
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que dictæ figuræ ſint circuli, iuxta alibi à me oſtenſa.</
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<
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">Pariter ſi figuræ genitrices ſolidorum ſint circuli, vel ellipſes, illæ
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autem, quæ dicuntur @omnes figuræ ſimiles earundem ſumptæ cum datis
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regulis) ſint pariter circuli, quorum deſcribentes rectæ lineæ in figuris
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genitricibus ſint eorundem diametri, ſolida ſimilaria genita ex eiſdem,
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iuxta eaſdem regulas, erunt, alterum ſpbæra, quod ſcilicet gignitur ex
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">_@6. Lib. 1._</
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circulo, alterum ſphæroides quod ſcilicet gignitur ex ellipſi, ſi figuræ
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ſimiles rectè ſecent axem ellipſis, & </
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</
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xlink:label
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">_47. Eiuſd._
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_lib. 1._</
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poterit etiam eſſe ſpbæroides, etiamſi figuræ ſimiles non ſint circuli, ſed
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ellipſes iuxta alibi oſtenſa; </
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<
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xml:space
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">quæ igitur in boc caſu nomine communi di-
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cuntur, ſolida ſimilaria genita ex circulo, vel ellipſi, iuxta datas regu-
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las, nomine particulari, & </
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<
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</
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<
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">Et quæ pariter dicerentur nomine communi ſolida ſimilaria genita ex
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portione tali, vel tali, iuxta talem regulam, portione inquam circuli,
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vel ellipſis, quotieſcunque figuræ, quæ dicuntur, omnes figuræ ſimiles
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talis portionis iuxta eandem regulam, ſint circuli erecti genitricibus,
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& </
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<
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proprio, portio ſphæræ; </
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<
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<
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guræ ſimiles ſint circuli erecti genitricibus, rectè axem portionis ſecan-
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tes, ſiet portio ſphæroidis, quod ſi ſint ellipſes erectæ genitricibus, dia-
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metros habentes, vt poſtulat Propoſ. </
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<
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<
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roidis: </
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<
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">Sic igitur nommibus particularibus hæc ſolida vocari conſuene-
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runt. </
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">Cum verò figuræ ſimiles non ſunt neq; </
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<
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ptæ, vt dictum eſt, ſufficiet eadem vocare nomine communi ſolidi ſimi-
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Laris, &</
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<
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<
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">nominationem ſimilium figurarum,
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conſequenter & </
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<
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">eadem varia ſolida, variè nominari poſſent; </
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<
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in ſequentibus ex genitricium figurarum variatione varia nomina com-
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ponemus, interim hæc teneantur, hoc animaduerſo, quod in ſuperiori-
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bus, dum ſit ſphæra, vel ſphæroides, vel eorundem portio, ſuppono li-
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neas, quæ ſunt in genitricibus ſiguris, & </
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