335142
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.
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.
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})
_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.
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.
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}; &
= √{_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}; &