336316GEOMETRIÆ
Quoniam ergo, OF, eſt diſtantia parallelarum axi ductarum à
punctis, BF, abſcindatur à, BF, recta, FE, æqualis diſtantiæ, F
O, inſuper intelligatur adhuc ipſa, CD, ducta vtcunque parallela
rectæ, BF, terminans in puncta, CD, curuæ parabolæ, & cum
ſit, VG, diſtantia parallelarumaxi, quæ à punctis, CD, ducun-
tur, abſcindatur ab ipſa, CD, verſus, D, ipſa, DZ, æqualis di-
ſtantiæ, VG; ſic ductis in portione, BCDF, omnibus lineis, regu-
la, BF, in earundem ſingulis intell gantur ſumptæ diſtantiæ, ſicut
acceptæ ſuerunt, EF, ZD, quarum extrema puncta ſint in curua
parabolica, FDCB, ſint autem in huius curuæ ea parte, in qua
ſunt puncta, DF, patet ergo ſi fumamus punctum, S, verticem
portionis, BSF, quod dictarum omnium linearum extrema puncta
erunt in curua parabolica, quæ incipit a vertice, S, & deſinit in, F;
226[Figure 226]
per alia ergo extrema puncta earundem
diſtantiarum intelligatur ducta linea, S
ZE. Dico figuram, SFE, compre-
henſam recta, EF, curua parabolica,
SDF, & linea, SZE, eſſe huiuſmo-
di, quod, ſi duxerimus intra ipſam vt-
cunq; ipſi, BF, parallelam, quæ pro-
ducatur vſq; ad curuam parabolicam,
huius portio manens in figura, SEF, erit diſtantia parallelarum
axi, quæ ducuntur ab extremis punctis ab eadem producta in curua
parabolica ſignatis. Intelligatur ergo ducta vtcunque, DZ, ipſi, B
F, parallela, & producta vſq; ad curuam parabolicam incidens illi
in puncto, C, quoniam ergo, CD, eſt vna earum, quæ dicuntur
omnes lineæ figurę, BSF, portio eiuſdem manens intra figuram,
SEF, erit diſtantia parallelarum axi, quę ab eiuſdem extremis pun-
ctis ductæ intelliguntur, & hoc per conſtructionem patet, quoniam
abipſa, CD, abſciſſa eſt, DZ, quę terminat in lineam, SZE, æ-
qualis dictę diſtantię, ergo figura, SEF, deſcripta eſt, qualem pro-
blema poſtulabat; quę vocetur figura diſtantiarum portionis, ſiue pa-
rabolę, BSF.
punctis, BF, abſcindatur à, BF, recta, FE, æqualis diſtantiæ, F
O, inſuper intelligatur adhuc ipſa, CD, ducta vtcunque parallela
rectæ, BF, terminans in puncta, CD, curuæ parabolæ, & cum
ſit, VG, diſtantia parallelarumaxi, quæ à punctis, CD, ducun-
tur, abſcindatur ab ipſa, CD, verſus, D, ipſa, DZ, æqualis di-
ſtantiæ, VG; ſic ductis in portione, BCDF, omnibus lineis, regu-
la, BF, in earundem ſingulis intell gantur ſumptæ diſtantiæ, ſicut
acceptæ ſuerunt, EF, ZD, quarum extrema puncta ſint in curua
parabolica, FDCB, ſint autem in huius curuæ ea parte, in qua
ſunt puncta, DF, patet ergo ſi fumamus punctum, S, verticem
portionis, BSF, quod dictarum omnium linearum extrema puncta
erunt in curua parabolica, quæ incipit a vertice, S, & deſinit in, F;
diſtantiarum intelligatur ducta linea, S
ZE. Dico figuram, SFE, compre-
henſam recta, EF, curua parabolica,
SDF, & linea, SZE, eſſe huiuſmo-
di, quod, ſi duxerimus intra ipſam vt-
cunq; ipſi, BF, parallelam, quæ pro-
ducatur vſq; ad curuam parabolicam,
huius portio manens in figura, SEF, erit diſtantia parallelarum
axi, quæ ducuntur ab extremis punctis ab eadem producta in curua
parabolica ſignatis. Intelligatur ergo ducta vtcunque, DZ, ipſi, B
F, parallela, & producta vſq; ad curuam parabolicam incidens illi
in puncto, C, quoniam ergo, CD, eſt vna earum, quæ dicuntur
omnes lineæ figurę, BSF, portio eiuſdem manens intra figuram,
SEF, erit diſtantia parallelarum axi, quę ab eiuſdem extremis pun-
ctis ductæ intelliguntur, & hoc per conſtructionem patet, quoniam
abipſa, CD, abſciſſa eſt, DZ, quę terminat in lineam, SZE, æ-
qualis dictę diſtantię, ergo figura, SEF, deſcripta eſt, qualem pro-
blema poſtulabat; quę vocetur figura diſtantiarum portionis, ſiue pa-
rabolę, BSF.
COROLLARIVM.
_Q_Via verò oſtenſum eſt, BF, ad diſtantiam parallelarum axià, B,
F, ductarum, eſſe vt, CD, ad diſtantiam parallelarum axi à
punctis, C, D, ductarum, ſunt autem, EF, ZD, æquales dictis diſtan-
tijs, ideò erit, BF, ad, FE, vt, CD, ad, DZ, & ſic erit quælibet du-
cta in portione, BSF, parallelaipſi, BF, adeiuſdem partemincluſam@
figura, SEF, vt, BF, ad, FE.
F, ductarum, eſſe vt, CD, ad diſtantiam parallelarum axi à
punctis, C, D, ductarum, ſunt autem, EF, ZD, æquales dictis diſtan-
tijs, ideò erit, BF, ad, FE, vt, CD, ad, DZ, & ſic erit quælibet du-
cta in portione, BSF, parallelaipſi, BF, adeiuſdem partemincluſam@
figura, SEF, vt, BF, ad, FE.
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