TRACT 1C.

WITHOUT TABLES.

265

a , a a a a* . ,

-p - ip f — =- 4p -1--- - &c : and

n 7 Sr n 1 Sr 480r s ’

a

A = n X (|P- -=«x(V(2-V(l-

S ) - nearly.

rr

4 1

Coral. 7.—And again, since —; x (p — q — \q l =

. , . a . . r a 4p— q

&c ; where q is = —; by subtracting this from --—=

— -q 6 &c, and reducing, there will be obtained A = —- x

tov iUO

{U4P-39q-^)=~x{lU^/2-2V(l-g l ))-S9q-^,

which will commonly give the angle exact to within a minuteof the truth. Where note, that the constant quantity ^ is— *54567409. And from the whole may be drawn the fol-lowing general problem.

PROBLEM.

To perform all the Cases of Trigonometry •without any Tables.

. Having any three, parts of a triangle given, except the threeangles, the other three parts may be found, by some of thefollowing six general theorems.

1 . A = in X {W (2 - V (- nearly. Or

A== f^ x ( 14 v (2 - v(i-i))- S9 T-575) more nearI y-

r 2 r l

_ a a* 3 a i 3.5a 7 3 5.7a 9 .

2. a = n x (—1_I-P-4-&c.)

r ^2.3r> 2.4.5r 5 2.4.6.7r 7 2.4.6.8.9r 9

3. a =

4. r =

VX ^n 2.3« 3 + 2.3.4. 5n s 2.3.4.5 .6.7« 7

&c.)

2.3. 2.3.4.5m s 2.3.4.5.6.7a 7

&C.