Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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erunt axes baſium eorundem ſolidorum, ipſarum nempè figurarum,
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ex 37. hu-
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ius.</
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FGHN, BDCE, ſunt. </
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<
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<
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">plana, FMH, BA
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C, per axes tranſeuntia ſunt baſibus erecta. </
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<
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">Sint autem ſolidorum
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iam dictorum axes, necnon axes, ſeu diametri figurarum, FMH,
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BAC, ipſæ, OM, XA. </
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<
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">Qura ergo ſiguræ, FMH, BAC, ſunt
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fimiles portionum coni ſectiones, quarum baſes, ſiue ad earum axes,
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vel diametros, MO, AX, ordinatim applicatæ ſunt, FH, BC, e-
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runt homologarum earundem regulæ, ac tangentes ipſas figuras ex
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vna parte, ex alia verò, quo per vertices, M, A, eiſdem ducentur æ-
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quidiſtantes, earundem verò oppoſitarum tangentium, acipſarum
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figurarum incidentes, MO, AX, eritque, FH, ad, BC, vt, MO,
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ad, AX. </
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<
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">Si ergo baſes, FGHN, BDCE, ſint circuli erunt figurę
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ſimiles, quarum & </
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<
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">oppoſitarum tangentium per extrema, FH, du-
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">Lẽma 31.
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huius.</
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ctarum incidentes fient diametri, FH, BC. </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0116-01
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lipſes, quoniam, FH, BC, ſunt axes,
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facilè probabimus, ſicut pro circulo fa-
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ctum eſt ad Lemma Propoſ. </
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<
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<
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auxilio Propoſ. </
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<
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<
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">huius, ipſas, FH,
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BC, eſſe incidentes ſimilium figurarum,
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FGHN, BDCE, & </
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<
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tangentium, quę per puncta, F, H; </
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">B,
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C, ducuntur (quę ipſis, FH, BC, exi-
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ſtent perpendiculares, cum ſint axes ea-
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rundem figurarum.) </
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<
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">Et eodem modo
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ſi dicta ſolida ſecentur alijs planis præ-
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fatis baſibus parallelis (ita tamen vt illa
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diuidant ſimiliter ad eandem partem ip-
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ſas, MO, AX, & </
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<
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">ſubinde etiam altitudines ipſorum ſolidorum re-
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Elem.</
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ſpectu dictarum baſium aſſumptas) oſtendemus & </
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<
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lidis figuras eſſe ſimiles, & </
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<
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">earum, ac oppoſitarum tangentium (æ-
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quidiſtantium tanquam regulis duabus oppoſitis tangentibus ba-
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ſium, FH, BC, per extrema, F, H; </
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<
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">B, C, iam ductarum) inci-
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dentes eſſe communes ipſarum ſectiones cum figuris, FMH, BAC,
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quæ omnes erunt lineæ homologæ ſimilium figurarum, FMH, B
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AC, quarum regulę, FH, BC. </
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<
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">Ergo, ductis per, M, A, duobus
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planis baſibus parallelis, quæ ipſa ſolida contingent, incidunt hiſce
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oppoſitis tangentibus planisad eundem angulum ex eadem parte
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plana figurarum, FMH, BAC, ſectis autem ſolidis planis paralle-
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lis, vt dictum eſt, fiunt in ipſis ſimiles figuræ planæ, & </
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dentes capiuntur omnes in ſimilibus figuris, FMH, BAC, quarum
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ſunt homologæ, earumque regulæ ipſæ, FH, BC, & </
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logæ figurarum homologarum duabus quibuſdam regulis, </
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