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

333140

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

11Fig. 215.

_cc_ + _ba_ - _aa_ = _nn._

_cca_ + _baa_ - _a_3 = _n_3.

_ccaa_ + _ba_3 - _a_4 = _n_4, & c.

_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-
22Fig. 215. 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.

Not.

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