303110
APPENDICULA 1.
HIc demùm etſi præter inſtitutum ſit particularia nunc attingere;
qualibus ſanè, hæc generalia conſequentibus, admodum pro-
clive foret turgidum Volumen compingere (_amico tamen morem ge-_
_rens operâ_ dignum cenſenti) ſubtexam ad _Circuli Tangentes Secantéſq_;
ſpectantia nonnulla, pleraque de ſuprà poſitis emergentia.
qualibus ſanè, hæc generalia conſequentibus, admodum pro-
clive foret turgidum Volumen compingere (_amico tamen morem ge-_
_rens operâ_ dignum cenſenti) ſubtexam ad _Circuli Tangentes Secantéſq_;
ſpectantia nonnulla, pleraque de ſuprà poſitis emergentia.
11Fig. 166.
Eſto _cirtuli Quadrans_ ACB, quam tangant rectæ AH, BG;
&
in productis HA, AC ſumantur AK, CE ſingulæ pares _radio_ CA;
& _aſymptotis_ AC, CZ per K deſcripta ſit _Hyperbola_ KZZ; _aſymp-_
_totis_ BC, BG per E _byperbola_ LEO. Sumatur etiam in arcu AB
22Fig. 167. _punctum arbitrarium_ M, per quod ducantur recta CMS (tangenti
AH occurrens in S) recta MT circulum tangens; recta MFZ ad
BC parallela, recta MPL ad AC parallela. Sit denuò recta α β æ-
qualis _arcui_ AB, & α μ arcui AM; & rectæ α γ, ξ μ π ψ rectæ α β
perpendiculares; quarum α γ = AC; μξ = AS; μψ = CS; μπ
= MP.
in productis HA, AC ſumantur AK, CE ſingulæ pares _radio_ CA;
& _aſymptotis_ AC, CZ per K deſcripta ſit _Hyperbola_ KZZ; _aſymp-_
_totis_ BC, BG per E _byperbola_ LEO. Sumatur etiam in arcu AB
22Fig. 167. _punctum arbitrarium_ M, per quod ducantur recta CMS (tangenti
AH occurrens in S) recta MT circulum tangens; recta MFZ ad
BC parallela, recta MPL ad AC parallela. Sit denuò recta α β æ-
qualis _arcui_ AB, & α μ arcui AM; & rectæ α γ, ξ μ π ψ rectæ α β
perpendiculares; quarum α γ = AC; μξ = AS; μψ = CS; μπ
= MP.
I.
Recta CS æquatur rectæ FZ;
adeoque _ſumma ſecantium ad_
_arcum_ AM pertinentium, & ad rectam AC applicatarum æquatur
_ſpatio byperbolico_ AF ZK.
_arcum_ AM pertinentium, & ad rectam AC applicatarum æquatur
_ſpatio byperbolico_ AF ZK.
Eſt enim CF.
CA:
: (CM.
CS:
:) CA.
CS.
adeòque CF
x CS = CAq. item CF x FZ = CA x AK = CAq. ergo CS = FZ.
x CS = CAq. item CF x FZ = CA x AK = CAq. ergo CS = FZ.
II.
_Spatium_ αμξ (hoc eſt _Smmma tangentium in arcu_ AM ad re-
33Fig. 167. ctam αμ applicatarum) æquatur _ſpatio byperbolico_ AFZK.
33Fig. 167. ctam αμ applicatarum) æquatur _ſpatio byperbolico_ AFZK.