Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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<
s
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xml:space
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">Quoniam ergo, OF, eſt diſtantia parallelarum axi ductarum à
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punctis, BF, abſcindatur à, BF, recta, FE, æqualis diſtantiæ, F
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O, inſuper intelligatur adhuc ipſa, CD, ducta vtcunque parallela
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rectæ, BF, terminans in puncta, CD, curuæ parabolæ, & </
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<
s
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xml:space
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ſit, VG, diſtantia parallelarumaxi, quæ à punctis, CD, ducun-
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tur, abſcindatur ab ipſa, CD, verſus, D, ipſa, DZ, æqualis di-
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ſtantiæ, VG; </
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<
s
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echoid-s7619
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xml:space
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">ſic ductis in portione, BCDF, omnibus lineis, regu-
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la, BF, in earundem ſingulis intell gantur ſumptæ diſtantiæ, ſicut
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acceptæ ſuerunt, EF, ZD, quarum extrema puncta ſint in curua
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parabolica, FDCB, ſint autem in huius curuæ ea parte, in qua
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ſunt puncta, DF, patet ergo ſi fumamus punctum, S, verticem
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portionis, BSF, quod dictarum omnium linearum extrema puncta
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erunt in curua parabolica, quæ incipit a vertice, S, & </
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<
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">deſinit in, F;
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per alia ergo extrema puncta earundem
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diſtantiarum intelligatur ducta linea, S
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ZE. </
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<
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xml:space
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">Dico figuram, SFE, compre-
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henſam recta, EF, curua parabolica,
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SDF, & </
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<
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xml:space
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">linea, SZE, eſſe huiuſmo-
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di, quod, ſi duxerimus intra ipſam vt-
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cunq; </
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<
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xml:space
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">ipſi, BF, parallelam, quæ pro-
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ducatur vſq; </
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<
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xml:space
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">ad curuam parabolicam,
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huius portio manens in figura, SEF, erit diſtantia parallelarum
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axi, quæ ducuntur ab extremis punctis ab eadem producta in curua
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parabolica ſignatis. </
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<
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xml:space
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">Intelligatur ergo ducta vtcunque, DZ, ipſi, B
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F, parallela, & </
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">producta vſq; </
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<
s
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xml:space
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">ad curuam parabolicam incidens illi
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in puncto, C, quoniam ergo, CD, eſt vna earum, quæ dicuntur
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omnes lineæ figurę, BSF, portio eiuſdem manens intra figuram,
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SEF, erit diſtantia parallelarum axi, quę ab eiuſdem extremis pun-
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ctis ductæ intelliguntur, & </
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<
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">hoc per conſtructionem patet, quoniam
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abipſa, CD, abſciſſa eſt, DZ, quę terminat in lineam, SZE, æ-
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qualis dictę diſtantię, ergo figura, SEF, deſcripta eſt, qualem pro-
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blema poſtulabat; </
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<
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xml:space
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">quę vocetur figura diſtantiarum portionis, ſiue pa-
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rabolę, BSF.</
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<
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">_Q_Via verò oſtenſum eſt, BF, ad diſtantiam parallelarum axià, B,
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F, ductarum, eſſe vt, CD, ad diſtantiam parallelarum axi à
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punctis, C, D, ductarum, ſunt autem, EF, ZD, æquales dictis diſtan-
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tijs, ideò erit, BF, ad, FE, vt, CD, ad, DZ, & </
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<
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">ſic erit quælibet du-
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cta in portione, BSF, parallelaipſi, BF, adeiuſdem partemincluſam@
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figura, SEF, vt, BF, ad, FE.</
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