Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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cuitum figurarum eodem ordine ſumptas, ita ſe habere, ve-
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lut illæ, quæ dictis tangentibus inciderunt, iſtæ, quæ illis
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inciderunt, erunt tum ſimilium propoſitarum figurarum, tum
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ductarum tangentium, incidentes.</
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<
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<
s
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">ſimiles planę figurę, ACEI, MTVS, qua-
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rum ſint ductæ oppoſitæ tangentes homologarum earundem regu-
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læ, AB, EF, figuræ, AE, &</
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<
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">, MN, VR, figurę, MV, incidant
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autem eiſdem ad eundem angulum ex eadem parte duæ, BF, NR,
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& </
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<
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">ductæ ſint quædam duæ ipſis tangentibus parallelæ, CD, TO,
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ſecantes ipſas, BF, NR, (& </
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<
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">coniequenter incidentes, vt facilè
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patet) ſimiliter ad eandem partem, reperiamus, CD, ad, TO, & </
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<
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pariter, ID, ad, SO, eſſe vt, BF, ad, NR. </
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<
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">Dico ipſas, BF, N
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R, eſſe incidentes ſimilium figurarum, AE, MV, & </
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<
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poſitarum tangentium, VR, MN;
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">Ex dictis igitur ipſę, CI, T
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">C. 10. defi.
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mitionis.</
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S, erunt homologę earundem ſimilium
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figurarum, AE, MV, & </
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<
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">Ex cor. 2.
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19. & 22.
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huius.</
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ad, TO, eſt vt, BF, ad, NR, &</
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<
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F, ad, NR, vt, ID, ad, SO, erit, C
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D, ad, TO, vt, ID, ad, SO, igitur
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puncta, D, O, reperientur in duabus
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dictarum fimilium figurarum, & </
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<
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poſitarum tangentium, incidentibus,
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ſint illæ ipſæ, HG, PL, quę cum ip-
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ſis, TO, CD, æquales angulos ad
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eandem partem continebunt. </
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<
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men etiam ipſas, NR, BF, eſſe ea-
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rundem figurarum, & </
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<
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cidentes: </
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<
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">Sint puncta contactus tangentium, FE, RV, proxima ip-
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ſis, NR, BF, ipſa, V, E. </
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<
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">Dico, EF, ad, VR, eſſe vt, FB, ad,
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<
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10.</
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RN, nam, EL, ad, VG, eſt vt, LP, ad, GH, quia verò angu-
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lus, CDP, æquatur angulo, TOH, &</
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<
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">, CDB, ipſi, TON, re-
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liquus, PDB, ęquabitur reliquo, HON, & </
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<
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">ſic etiam, FDL, ipſi,
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ROG, eſt etiam angulus, PLE, ęqualis angulo, HGV, ideò re-
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<
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Elem.</
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liquus in triangulo, DFL, ideſt angulus, DFL, erit ęqualis angu-
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lo, ORG, & </
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<
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">ſic triangula, FDL, ORG, erunt æquiangula, vt
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etiam probabimus triangula, DPB, OHN, eſſe ęquiangula, ſicut
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ſunt ęquiangula inter ſetriangula, FDL, PDB, &</
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<
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">, ROG, HO
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N, vnde vt, LD, ad, DF, ſic erit, PD, ad, DB, permutando,
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LD, ad, DP, erit vt, FD, ad, DB, componendo, LP, ad, PD,
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erit vt, FB, ad, BD, permutando, LP, ad, FB, erit vt, PD, </
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