Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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28390 VDq + EIq + FKq + GLq; ergò ſumma IXq +
KXq
+ LXq + HXq, ſubdupla eſt ſummæ VDq - EIq +
FKq
+ GLq.
Vnde liquet Propoſitum.
XV. Quòd ſi curva DXH talis concipiatur, ut ſit ordinata quæpiam,
ceu
IX, inter congruas ordinatas IE, IZ bimedia *;
erit ſumma cubo-
rum
ex IX, KX, LX, &
c. ſubtripla cuborum ex DV, IE, KF, & c. Sin IX
ſit
trimed.
* erit IXqq + KXqq + LXqq, & c. = {DVqq + IEqq + KFqq/4}
&
c. ac ità porrò quoad cæteras poteſtates. * _Not._ bimediam ap-
pello
, quæ duarum mediarum proportionalium prima;
trimediam,
quæ
trium prima eſt, &
c.
XVI. Sit porrò linea VYQ talis, ut ordinata AY ipſi AT; &
ordinata
BY ipſi BT, &
c. æquentur; erit IZq + KZq + LZq,
&
c. (ſumma quadratorum ex ordinatis à curva DZO ad rectam DH)
æqualis
ſummæ VA x AE x AY + AB x BF x BY + BC x CG
x
CY, &
c. (hoc eſt figuræ VDH in figuram VDQ ductæ).
XVII. Item, ſumma IZ. cub. + KZ cub. + LZ cub. & c. =
VA
x AE x AYq + AB x BE x BYq + BC x CG x CYq,
&
c. _hoc eſt figuræ_ VDH _in figuræ_ VDQ _quadrata ductæ_). Simi-
lis
&
aliarum _poteſtatum_ eſt ratio.

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