of the Angle fubt ended by Two Ohje&s, &c. 421 
From thefe geometrical proportions,, having given any arc and 
the variation of its fine or cofine, the cotemporary variation of 
the arc may be efUmated by computation in general for any 
cofine = c 9 the chord of the arc’s variation — x 9 the given varia- 
tion of the coline — d 9 or the given variation of the fine dr#. 
ference d 9 the chord of the cotemporary decreafe of the arc, or 
which are the mathematically true values of the chord FB, 
and will approximate to the magnitude of the arc FB as that 
arc is continually diminifhed. The following expreffions for 
the chord of the variation x are more compendious, and will 
be fupciently near the truth whenFB is very fmall. 
be a decrement, the fign of x and of b or d mull be changed. 
26. Let the quantities p 9 s, m 9 n 9 vary by fmall in- 
rary variation of cof ED, becaufe (art. 21.) 
Cof. ED = 1 — 8 s z p z x 1 — s" p~ — in + ni n" + tn z p z — 2 p 1 nfrf + 
part of the quadrant. Let the fine of any arc be s, '•the 
radius = 1 ; then if the cofine of the arc increafes by the dif- 
— x = v 2S Z — 2 dc ^ \/ 2s~ — 2 dc — ^d z 
and if the fine of the given arc increafes by the difference b 
In thefe four expreffions it muft be obferved, that the fine and 
cofine are fuppofed to vary by increafe : fhould the variation 
crements/>, s, m, n 9 refpeclively, then to obtain the cotempo- 
tn z n z s z p 1 - ±z 2 m z np x %/ 1 —p z x/i -fx/i-f 
by taking the fluxion of the equation we have 
Von. LXXI. 
K k k 
Cof 
