Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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milium. </
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xml:space
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">Ducantur plana oppoſita tangentia cylindrici, AM, re-
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huius.</
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ſpectu plani, BF, in eo ducti, vnius quorum, & </
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<
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rum, YNO, TDF, productorum, communes ſectiones ſint, XS,
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MG, alterius autem, & </
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<
s
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xml:space
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">eorundem planorum ſint rectæ, YP, TQ,
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indefinitè ambæ productæ, ſumpto autem in, YP, vtcumque pun-
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cto, P, ducatur per, P, ipſi, CF, æquidiſtans, PQ, & </
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<
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">ab eodem
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in plano per, YP, XS, tranſeunte vſquead, XS, ducatur vtcum-
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queipſa, PS, per ipſas autem, QP, PS, intelligatur extenſum pla-
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num, quod ſecetaliud tangens planum in, SG, & </
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<
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Q, MG, ductum in, QG, producan-
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tur autem ipſæ, NO, DF, verſus, P
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S, QG, quibus occurrant in, V, R,
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& </
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<
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">iungatur, VR, erunt igitur, VR,
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PQ, communes ſectiones æquidiſtan-
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tium planorum, YQ, NR, & </
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<
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PR, & </
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<
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">ideò erunt parallelæ, vt & </
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<
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ſæ, PV, QR, &</
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<
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logrammum: </
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<
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</
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<
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xml:space
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">oſtendemus eſſe parallelogramma ip-
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ſa, VG, PG, NF, OR, NR, & </
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<
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xml:space
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gulum, PSX, æqualem eſſe angulo,
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QGM, & </
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<
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xml:space
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<
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xml:space
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">B. Def. 10.
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huius.</
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cidentes ſimilium figurarum, YNO,
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TDF, & </
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<
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gentes eſſe homologarum earundem regulas, & </
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<
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xml:space
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">quia eiſdem æqui-
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diſtant ipſæ, NO, DF, & </
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<
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<
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tem ipſas incidentes, PS, QG, diuidunt; </
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<
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xml:space
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QR, &</
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<
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">, VS, ipſi, RG, ideò ipſæ, NO, DF, erunt lineæ homo-
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logæ figurarum, YNO, TDF, ſimilium, quæ in plures homolo-
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gas ſecari contingere poteſt, prout ſe habet ambitus ſuperficiei cy-
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lindraceæ huius cylindrici, AM, ſunt lineæ homologæ inquam, ſi
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xml:space
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">C. Def. 10.
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huius.</
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ſint intra ambitum figurarum, quarum ſunt homologæ, ſunt verò
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latera homologa, ſi ſint in earundem ambitu, veluti contingeret ſi
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planum per latera ductum eſſet planum contactus vnius oppoſito-
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rum tangentium, veluti ſi cylindricus fuiſſet, cuius oppoſitæ baſes
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ſunt, ABC, TDF, excluſis reſiduis figuris, quæ ab ipſis, BC, D
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F, abſcinduntur, tunc enim eodem modo facta fuiſſet demonſtra-
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tio, vt conſideranti facilè patebit; </
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<
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& </
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<
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bus æquidiſtantium, & </
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<
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">parallelogrammi, BF, probantes ſcilicet
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eaſdem eſſe lineas, vellatera homologa figurarum in cylindrico per
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baſibus æquidiſtantia plana productarum, quod oſtendere opus erat.</
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