Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBERI.
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DB, ideſt vt, HO, ad, ON, at, vt ſupra, oſtendemus, HO, ad,
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ON, eſſe vt, HG, ad, NR, ergo, PL, ad, BF, erit vt, HG,
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ad, NR, erat autem, EL, ad VG, vt, PL, ad, HG, ergo, EL,
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ad, VG, erit vt, BF, ad, NR, quia verò, BF, ad, NR, eſt vt,
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DF, ad, OR, (nam, BF, NR, ſunt ſimiliter diuiſæ in punctis,
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D, O,) ideſt vt, FL, ad, RG, ergo, EL, ad, VG, erit vt, FL,
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ad, RG, ergo reliqua, EF, ad, VR, erit vt tota, EL, ad, VG,
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ideſt vt, BF, ad, NR. </
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<
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">Idem oſtendemus de quibuslibet ductis ip-
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ſis, EF, VG, parallelis, quę diuidant, BF, NR, ſimiliter ad ean-
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dem partem, nempè eas, quæ inter ipſas, BF, NR, & </
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<
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">circuitum
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figurarum, AE, MV, eodem ordine ſumptæ continentur, eſſe vt
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ipias, BF, NR, ergo, BF, NR, ſunt incidentes ſimilium figura-
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<
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">B. Def. 10.</
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rum, MV, AE, & </
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">ductarum tangentium, quod oſtendere opus erat.</
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">INnoteſcit exhoe conſequenter duarum ſimilium figurarum, & </
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<
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">ea-
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rundem oppoſitarum tangentium, quæ ſuntregulæ homologarum,
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tum incidentes ſimiliter diuidi ab homologis earundem figurarum, pro-
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ductis, ſi opus ſit, tum quaſcumque alias, quæ cum homologis angulos
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continent æquales, vt exempli gratia ipſæ, NR, BF. </
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<
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xml:space
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">Et vlterius ip-
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ſas homologas eſſe tum vt quaſuis incidentes, tum vt eiſdem parallelas,
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ideſt ex. </
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">gr. </
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">CI, ad, TS, mdum erit vt, PE, ad, HG, ſiue vt, BF, ad,
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NR, ſed etiam vt, BF, ad quamcumque aliam parallolam ipſi, NR,
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ductam inter parattelas, MN, VR, nam illa erit æqualis ipſi, NR.
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</
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<
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">Patet igitur duarum ſimilium figurarum homologas nedum eſſe vt ea-
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rum, & </
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">oppoſitarum earundem tangentium, quæ ſunt regulæ homolo-
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garum, incidentes, ſed etiam vt quaſuis alias inter eaſdem tangentes
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ductas ipſis incidentibus æquidiſtantes, ſiue ad homologas ſimilium figu-
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rarum æqualiter inclinatas.</
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<
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">THEOREMA XXII. PROPOS. XXV.</
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<
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">SI quæcunque ſimiles figuræ planæ à rectis lineis deſcti-
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bantur, quæ ſint earundem homologæ, & </
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<
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les; </
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">ſuperponantur autem ad inuicem ipſæ figuræ, ita vt ea-
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ſdem deſcribentes rectæ lineæ ſibi congruant, figuræq; </
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<
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fimiliter poſitæ, illæ quoque erunt ad inuicem congruentes.</
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<
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">Sint ſimiles figuræ planæ, ABXC, EFPG, quæcunq; </
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<
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ptæ ab earundern homologis, & </
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