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

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Series undecima.

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

_cc_ - _ba_ - _aa_ = _nn_.

_cca_ - _baa_ - _a_3 = _n_3.

_ccaa_ - _ba_3 - _a_4 = _n_4, & c.

In recta BAH ſumatur BA = _b_; & in AD ad AH perpendi-
11Fig. 216. culari ſit AC = _c_; ſintque anguli HAR, HBS ſemirecti; tum
utcunque ductâ GK ξ ad AH perpendiculari (quæ ipſam BS
ſecet in ξ; ſit AG. AC: : AC. ξK; & per K intra _aſymptotos_
VD, VS deſcribatur _hyperbola_ KYHK; ſint demum curvæ CLHLλ,
AMHMμ, ANHNν tales, ut inter AG (vel GZ) & GK ſint _me_-
_dia_ GL, _bimedia_ GM, _trimedia_ GN; hæ propoſito ſervient. id
quod conſtat, ut in præcedentibus.

Not.

1. Curvæ HLλ, HMμ, HNν ad decimam ſeriem pertinent;
reliquæ CLH, AMH, ANH ad undecimam.

2. Curva HL λ eſt _hyperbola æquilatera_, & curva CLH _circula_-
_ris circumferentiæ_ pars; utriuſque commune centrum eſt O, ipſam AB
biſecans (unde AH = √{_bb_/4} + _cc_: - {_b_/2})

3. In decima ſerie radix una ſemper habetur, & unica; in undeci-
ma nunc duæ, nunc una, ſubinde nulla.

4. Aφ = {_cc_/_b_}; & Aψ = √{_bb_/16} + {_cc_/2}: - {_b_/4}; & ordinentur
φ Y, ψ X; puncta Y, X ſunt nodi curvarum.

5. In undecimæ ſecundo gradu ordinata AC eſt maxìma; ſin AP
= √{_bb_/9} + {_cc_/3}: - {_b_/3}; & à P ad curvam AMH ordinetur Pγ,
hæc maxima erit; item ſi AQ = √{9_bb_/64} + {_cc_/2}: - {3_b_/8}; &

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