333140
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,
radicem dari; alioquin in omnibus una ſemper habetur, & unica;
quoniam recta EF curvas ſemel interſecabit, nec pluries,
Series octava.
{_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.
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-
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.
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.
1.
Curvæ CLH, AMH, ANH ad octavam ſeriem pertinent, re-
liquæ verò HLλ, HMμ, HN@, ad nonam.
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}
ad curvam CLH eſt OT maxima; ſin ſiat AP = {_b_/3} + √{_bb_/9}
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