[ 5 6 5 J 
XX. Let c be the chord of an arc {a) of the circumference of a circle, 
whofe diameter is d. Put N = 
where A, B , C , ftand for the refpective preceding terms. 
As the preceding theorems are eafily deduced from the fir ft, io the following are rnofl 
readily feen to be the immediate confequences of thefe ; and all depending upon no 
other principles than what are generally made ufe of in common computations. 
XXL Putting s, s\ t , t\ J f\ for the fine, co-fine, tangent, 
co-tangent, fecant, co-fecant, of an arc (a), and v its verfed fine j 
i*t ? - b f = M'r r = f = zf&c. n = -± . 
Then s ~ i — q"N -j- q' v N 2 — * q vf N 3 - \-q r,ll N + -(- q x N 5 , (Sc. X a. 
— a — ^'a^r— 3, -f- q 1 v 'a 5 r — 4 — q yf a 7 r—' q v, "a 9 r— t i (Sc. 
— a — — AN + ^ BN— ^ CN -f ^ DN, &e. where AM (Sc. 
ftand for the refpedtive preceding terms. 
And s' — r — ■ q'a z r~~ l -f -j'Vr - 3 — q v a 6 r—* -j- qJ"a % r~-\ (Sc. 
= i —q'N+ q"'N 2 — q'N* -f q YI W* 2 ’ X 2V$ 5 &V. x r. 
= rl-d A ^JV— A jJAT-f JL CN, (Sc. ABA as Before. 
' XXII. Alfo — q'a 2 r— 1 — q v a^r~ 3 -f- q v 'a 6 r~~ li — q r " , a*r~\ (Sc. 
(j . = T to. 
re — A' — - .iff- -LBN— LCN, to. X r. J,B,C, to. as before. 
3.2 3 .* 5.0 7.8 
XXIII. Let ;#=+?' — j" An dA=-A 
\Aq B'=—B—AA 
~ ? v ' +M—A<i" C=~C—BA -AB' 
D~-q vn Af ,,l -f^- JB f , +Aq\ D’^-D-CA—BB’—AC. 
(Sc. (Sc. 
Tangent / — 0 -f* Ba^r~* + Ca 7 r— 6 -j- Da9r~”*> (Sc. 
Or -1 + AN -jr BN 2 ~ CN 3 -j- DN 4 -}- EN r \iSc. x a. 
■ To-tangent i — a ~'r 2 -J~ A a -j- B'a^r— X -f~ C'a 5 r~* ~p D f a 7 r-~ r \ {Sc. 
Or ~^rr -J- A a 2 J r B'Na 2 A C'N 2 a z -j- D'N 3 a z , (Sc, > L. 
XXIV. 
