[ 5&3 J 
* *1 ,h£ "-*!■«• < f ■ 4 <S*. 
. . or i arcs > # & ^ err. whole number is the radium 
r a f S iF Qt ^l OT the P rodu<a °f ^he & co-fines, d^r fo- the 
.rX'f L p,o ?" as ma<,c ° f '3"y ^ "«y tie, t’J, 6-n'ti t 
S~» koni^. ’ *~b&c-) co-fines, where the co-fine noted by 
Ji 
Then the fine of «-f ,fev. =S— 6' ,, '-j- S r —S''\& 7 . x — j- 
And the co-fine of £*<■. —5 — S" , «V x_J__. 
1 3 «!— 1 
f// X r ; ' 7 !? r ' foi ; the fu f m of the tangents of the arcs, «, *. ,., ^r. 
^.Lglnts, and i= C 5 m ° f ’ * pr ° du£tS Qf CVCry two > thrcc > four » 
B=JT' — 5p'i 
C=BT"— J2*^- <f 
D=CT" — B c t' , '-\- AT 1 ' 2 ^" 
B—DT"— CP’+Br* 1 -' 4r"'~L<r x . Put R=— 
£sfc. 
Then the tangent of «+^+>-H, &>, — A-j-BR+CR^-j-DRi-^ERi &?<•. 
JrILk ’ t J? e , fine * tan § ent * and f ccant, of any arc g, being re- 
refentedby s, t,f, the co-fine, co-tangent, and co-fecant, by j\ t\ A 
aote ot the arc na are exprefled as in the following theorems. 
Putting u M ^=n",^ % n"=u'«.”Cp , ^ 
r 4 
Sine of na = »/?— n"AP~\-ri’BP—n*'CP- J r »' '"DP, Wc 7 x 
S 
J **— ■» 
r*-* 
J “ 
where P = SL. A=s-, B = AP-, C- BP-, D~CP-, &c. 
CP t?r. x 
't 
i Or — n^JZl.’Lzl A p 4-*-Z3.!^4 £iJ 
2 3 •'*‘ r > 6 v ,_r * 
.fill ' ' 
where yf, A, C, £jfr. ftand for the refpeftive preceding terms. 
0 . w.. 
where \ A> Z?,C, &V. ftand as before, 
M 
Dddd 
XVII. 
