Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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<
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<
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<
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<
s
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xml:space
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">(ijſdem vtibi conſtructis) duo oppoſita plana parallela tangentia fi-
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guras, AV, Κ Λ, ipſa, BD, HV; </
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<
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<
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">Λ, quibus incidunt pla-
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na figurarum ſimilium, AV, Κ Λ, ęquè ad eandem partem inclina-
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ta, quæ ſint nobis tanquam prima, ijſdem autem incidunt etiam ſe-
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cunda plana prima diuidentia, nempè plana, AGH, KYT, anguli
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autem, HGV, & </
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<
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xml:space
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">Υ Λ, ſunt æquales, qui nempè continentur com-
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munibus ſectionibus primorum, & </
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<
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nis, HV, & </
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<
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">Λ, quæ ſunt duo parallelorum planorum, ſimiliter an-
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guli, AGV, Κ Υ Λ, (contenti communibus ſectionibus primorum,
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& </
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<
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<
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<
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norum, & </
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<
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">ipſorum, HV, & </
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<
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<
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<
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gurarum, AV, Κ Λ, ergo etiam anguli, AGH, KY &</
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<
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">, æquales
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erunt, vt in Propoſ.</
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<
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<
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xml:space
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">iam oſtenſum eſt. </
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<
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xml:space
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">Cum autem figurę, AV,
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Κ Λ, ſint ſimiles, &</
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<
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">, AG, KY, latera homologa, erit, AG, ad,
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GV, vt, KY, ad, Υ Λ, oſtendemus autem eadem ratione, VG, ad,
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GH, eſſe vt, Λ Υ, ad, Y &</
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<
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">, ergo ex ęquali, AG, ad, GH, erit vt,
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KY, ad, Y &</
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<
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">. Eodem modo probabimus angulos, DVN, Q Λ ℟,
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ęquales eſſe (ſiue plana, AH, DN; </
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<
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<
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non, hoc.</
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<
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<
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">nihil refert) & </
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<
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">circa eos latera eſſe proportionalia, quod
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oſtendere opus erat.</
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">SI in ſimilibus rectilineis figuris, iuxta Euclidem, ducantur rectæ
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lineæ quęcumque, earundem latera homologa ſimiliter ad ean-
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dem partem diuidentes, ipſę diuident eaſdem in ſimiles figuras, ſimi-
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les autem erunt, quę ad eandem partem diuidentium linearum con-
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ſtituentur, & </
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<
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<
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ACED, GMNH, quibus incidant rectæ, B
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F, IO, ſecantes latera homologa, AC, GM;
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</
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tem, vt, AC, GM, in punctis, B, I, &</
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<
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HN, in punctis, F, O. </
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<
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conſtitutas ad eandem partem, nempè, BAD
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F, IGHO; </
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les eſſe. </
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<
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oppoſitos rectæ lineæ, BD, BE, IH, IN, vt
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ſi figuræ ſint quadrilateræ, vel multilateræ, in
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triangula diſceparentur. </
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<
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GM, ſimiliter diuiduntur in, B, I, erit, BA, ad, IG, vt, AC, </
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