Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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vel, DC, planum per, EM, XR, ductum æquidiſtabit plauo, AC,
<
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eſt autem planum, quod tangit cylindricum in, O, æquidiſtans pla-
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no, AC, & </
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<
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">tranſit per idem punctum, O, per quod tranſit planum
<
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per, EM, XR, ductum, ergo illa duo plana fiunt vnum planum,
<
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iacet autem, EM, in plano per, EM, XR, ducto, ergo iacet etiam
<
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in plano ęquidiſtante ipſi, AC, & </
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<
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xml:space
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">cylindricum, AC, tangente, igi-
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tur tangit cylindricum in recta, EM. </
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<
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">Eodem pacto ſi in alio pun-
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cto extra, EM, in ſuperficie cylindracea ſumpto tangeret cylindri-
<
lb
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cum, AC, oſtenderemus tangere ipſum in latere, quod per tale pun-
<
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ctum tranſiret; </
s
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<
s
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xml:space
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">in quo caſu tangeret cylindricum in lateribus vno
<
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pluribus, vt contingere poteſt. </
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<
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xml:space
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">Tangat autem ſecundò ipſum in
<
lb
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plano, igitur in eo plano ſnmpto vtcumque puncto, tanget cylindri-
<
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/>
cum in latere tranſeunte per tale punctum, igitur planum contactus
<
lb
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tale eſt, vt in eo omnes ductæ rectæ lineæ æquidiſtantes ipſi, EM,
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ſint latera cylindrici, AC, & </
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>
<
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">ſubinde eidem, EM, æqualia, vnde
<
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ſuperſicies, in qua iacent erit parallelogrammum, igitur planum
<
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contactus in hoc caſu erit parallelogrammum, & </
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<
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">erit æquiangulum
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parallelogrammo, AC, nam eius latera ſunt parallela lateribus pa-
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rallelogrammi, AC, & </
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<
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">ideò continent angulos æquales contentis
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à lateribus parallelogrammi, AC, vnde talia parallelogramma ſunt
<
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æquiangula, igitur contactus plani æquidiſtantis plano per latera
<
lb
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cylindrici ducto, vel fit in latere, aut lateribus contacti cylindrici,
<
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vel in parallelogrammo, ſiue parallelogrammis, in eiuſdem ſuper-
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ficie iacentibus, & </
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quod oſtendendum erat.</
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poſitarum baſium productorum planorum, quæ ſint, VF, XR,
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eſſe inter ſe parallelas, & </
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baſim, EAD, &</
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">SI cylindricus quomodocumque ſecetur per latera, diui-
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ditur in cylindricos à ſecantibus planis, ſi autem ſecetur
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planis omnibus eiuſdem lateribus coincidentibus inter ſe
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parallelis; </
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figuris, & </
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