Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

XXI. Porrò, ſit _circuli_ (cujus centrum C) ſegmentum BAE, cu-
jus axis AD, & _gravitatis centrum_ K; ponatur autem AD =
{_s_/_t_} CA, & HD = {2 _t_ - _s_/5 _t_ - 3 _s_} AD; erit HD major ipsâ KD.

Nam per H ducatur recta OP ad BE parallela; éſtque punctum
H centrum _gravitatis paraboliformis_, (puta AF B) ad baſin B E conſtitutæ, cujus exponens {_t_ - _s_/2 _t_ - _s_} & quæ proinde circulum AEB tangit; (nam ſi {_t_ - _s_/2 _t_ - _s_} = {_n_/_m_}; erit {2 _t_ - _s_/5 _t_ - 3 _s_} = {_m_/_n_ + 2 _m_}) & pro-
inde H erit centrum gravitatis _paraboliformis_ iſti coordinatæ per O, P tranſeuntis, & ad baſin BE pertingentis. Hæc autem ſupra O
P extra _circulum_ cadit, & infra OP intra ipſum; adeóque punctum H ſupra K ſitum eſt.

42.1.

Fig. 146.
2 _hujus ap._
8. _hujus ap._
10. _hujus ap_
11 _hujus ap_
4. _hujus ap._

XXII. Sin punctum L ſit _centrum gravitatis parabolæ_, erit L infra
K ſitum; adeóque KD & gt; {2/5} AD. Patet ex 4, & 17 hujus appen-
diculæ.

42.1.

Fig. 146.

XXIII. Sit _Hyperbolæ_ (cujus centrum C) _ſegmentum_ BAE, cujus
axis AD, baſis BE; gravitatis centrum K; ponatur autem AD =
{_s_ / _t_} CA, & HD = {2 _t_ + _s_/5 _t_ + 3 _s_} AD; erit HD minor ipsâ [?] KD.

42.1.

Fig. 147.

Nam per H ducatur recta OP ad BE parallela . Eſtque punctum H centrum gr. _paraboliformis_, puta AFB, ad baſin DB conſtitutæ,
cujus exponens {_t_ + _s_/2 _t_ + _s_}; quæ & _Hyperbolam_ ad B contingit (nam ſi {_t_ + _s_/2 _t_ + _s_} = {_n_/_m_}; erit {2 _t_ + _s_/5 _t_ +3 _s_} = {_m_/_n_ + 2_m_} quare H erit cen- trum gravitatis paraboliformis iſti coordinatæ per O, P ductæ, & ad BE
pertingentis. hæc autem ſupra OP intra hyperbolam cadit; & infra OP extra illam; inde pun@um K ſupra H exiſtit.

42.1.

2. _hujus. ap._
13. _hujus ap_
15. _hujus ap._
16 _hujus ap_
4. _hujus ap._

XXIV. Parabolæ centrum gr. (puta L) ſupra K exiſtit, adeóque
KD & lt; {2/3} AD. Patet ex 4, & 18 hujus appendiculæ.

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