## Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

4. Conſequentèr in harum ſecundo gradu ſin & gt;_ c_; in tertio, ſi _n_ 3
& gt; _cc_√{_cc_/3} - {_cc_/3} √ {_cc_/3} = {2/3}_cc_ √ {_cc_/3}; vel _n_ 6 & gt; {@@/27}_c_ [?] 6 ; in quar-
to ſi _n_ 4 & gt; {_c_ 4 /4} - {_c_ 4 /16} = {3/16}_c_ 4 ; nulla radix habetur; unam in iſtis
caſibus recta EF curvas ſupergreditur; nec iis occurrit.

5. Itidem in his omnibus maxima poſſibilis radix eſt AH = AC.

6. Curva CYH eſt _Circuli quadrans_, reliquæ AMH, ANH
quodammodo κυχλο{ει}δ{ετ}ς.

7. Ad ſextam ſeriem pertinentium curva HLL eſt _byperbola æqui_-
_latera_, cujus axis AH; reliquæ ſunt _Hyperboliformes_. Unde quoad
hanc ſeriem liquent cætera.

## 88.Series ſeptima.

_a_ + _b_ + {_cc_/_a_} = _n_.

_aa_ + _ba_ + _cc_ = _nn._

_a_ 3 + _baa_ + _cca_ = _n_ 3 .

_a_ 4 + _ba_ 3 + _ccaa_ = _n_ 4 , & c [?] .

In recta BAH indefinitè protensâ capiatur AB = _b_; & in AD
ad BH perpendiculari ſit AC = _c_; ſint etiam anguli HAR, HBS Semi-
recti; tum arbitrariè ductâ GY ad AH perpendiculari quæ ipſam
BS ſecet in Y; fiat AG. AC: : AC. YK; & per K intra angulum
DVS deſcribatur _hyperbola_ KKK; ſint demum curvæ CLL, AMM,
ANN tales, ut inter AG (vel GZ) & GK ſit _media_ GL, _bime_-
_dia_ GM, _trimedia_ GN; hæ ſatisfacient negotio. Nam eſt GK = _a_
+ _b_ + {_cc_/_a_}; & GLq = _aa_ + _ba_ + _cc_; & GMcub = _a_ 3 + _baa_
+ _cca_; & GNqq = _a_ 4 + _ba_ 3 + _ccaa_.

Fig. 214.

## 89.Not.

1. Secundi gradûs curva CLL eſt pars _hyperbolæ æquilateræ_, cujus
_centrum_ O, ipſam AB biſecans; & ſiquidem AC& gt; AO, eſt OH
(ad AB perpendicularis, &) = √ ACq - AO qejus _ſemiaxis_; ſin AC& lt; AO, ejus axis eſt OI = √ AOq - ACq. reliquæ
verò curvæ AMM, ANN ſunt _hyperboliformes_.

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