Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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colliguntur pro omnibus quadratis dictorum parallelogrammorum, pro
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omnibus quadratis etiam parabolarum eiſdem inſcriptiarum, tamquam
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pro earundem partibus proportionalibus, ſcilicet dimidijs, pariter vt
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vera recipi poſſunt.</
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<
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xml:space
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">B. SECTIO II.</
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xml:space
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">_E_T quia oſtenſum eſt omnia quadrata parallelogrammorum in ea-
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dem altitudine ſtantium, regulis baſibus, eſſe interſe, vt qua-
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drata baſium; </
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<
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xml:space
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">exiſtentium in eadem baſi eſſe, vt altitudines, vel
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etiam, vt latera eorundem æqualiter baſibus inclinata, ideò pariter hic
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colligemus omnia quadrata parabolarum in eadam altitudine exiſten-
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tium, regulis baſibus, eſſe vt quadrata baſium, & </
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dem baſis eſſe interſe, vt altitudines, vel vt diametros æqualiter ba-
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ſibus inclinatas.</
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<
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xml:space
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gulis baſibus, babere inter ſe rationem compoſitam ex ratione qua-
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dratorum baſium, & </
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">altitudinum, vel laterum æqualiter baſibus in-
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clinatorum; </
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">ideò colligemus, hic, omnia quadrata parabolarum regu-
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lis baſibus, babere inter ſe rationem compoſitam ex ratione quadrato-
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rum baſium, & </
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clinatorum.</
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<
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">_C_Onſimili metbodo colligemus, omnia quadrata parabolarum, regu-
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lis baſibus, quarum baſium quadrata alt itudinibus, vel diametris
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æqualiter baſibus inclinatis reciprocantur, eſſe æqualia, & </
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æqualia, eſſe parabolarum, quarum altitudines, vel diametri æquali-
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ter baſibus inclinatæ, baſium quadratis reciprocantur.</
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<
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<
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<
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">nempè omnia quadrata parabolarum,
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regulis baſibus, quarum altitudines, veldiametri, baſibus æ-
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qualiter inclinatæ, ad eaſdem baſes eandem rationem habeant, eſſe in-
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ter ſe in tripla ratione baſium, vel altitudinum, vel diametrorum
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æqualiter baſibus inclinatarum; </
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