Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

2. Hinc conſtat in ſecundo gradu ſi fuerit _n_& lt; C, nullam veram
radicem dari; alioquin in omnibus una ſemper habetur, & unica; quoniam recta EF curvas ſemel interſecabit, nec pluries,

90.Series octava.

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

Fig. 215.

_cc_ + _ba_ - _aa_ = _nn._

_cca_ + _baa_ - _a_ 3 = _n_ 3 .

_ccaa_ + _ba_ 3 - _a_ 4 = _n_ 4 , & c.

91.Series nona.

_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 AI ſumatur AB = _b_; & in AD ad ipſam AI perpen-
diculari ſit AC = _c_; fiant autem anguli IAR, ABS ſemirecti; ducatúrque recta ZGK ad AI utcunque perpendicularis, ipſam BS
ſecans ad ξ; & ſit AG. AC: : AC. ξ K; tum per K intra angu-
lum DSB deſcribatur _byperbola_ KYHK; ſint denuò curvæ CLHLλ,
AMHMμ, ANHNν tales, ut inter AG, GK ſint _media_ GL, _bime-_-
_dia_ GM, _trimedia_ GN; hæ curvæ propoſito ſatisfacient; conſtat
autem hoc ut in præcedente.

Fig. 215.

92.Not.

1. Curvæ CLH, AMH, ANH ad octavam ſeriem pertinent, re-
liquæ verò HLλ, HMμ, HN@, ad nonam.

2. Quoad octavam ſeriem, ſi biſecetur AB in O, & ordinetur OT
ad curvam CLH eſt OT maxima; ſin ſiat AP = {_b_/3} + √{_bb_/9} +

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