[ii9n 
32. In order to which 5 Put we, for the Radius of a 
Circle, the rightSineof an Arch or Angle, Ss the 
Verfed Sine, V; the Cp-Siue (or .Sine ot the Comple- 
ment) 2==R-V = V: Rq-Sq: the Secant , /s the Tan- 
gent, T. Fig. 4. 
33. Then is, 2.R::R./. That is, 2)R^(S = |^. the 
Secant 
34. And s.S::RT. That is, 2)SR (T = f ; the 
Tangent. 
Sy. Now, if we fuppofe the Radius CP, Fig. 7. di- 
vided into equal parts, (and each of them = <^ and, 
on thefe, to be erected the Co-Sines of Latitude LA: 
36. Then are the Sines of Latitude in ArithmeHck^ 
Progrellion. 
3 7. And the Secants anfwering thereunto, Lfz=z^^. 
38. But thefe Secants, (anfwering to right Sines in 
Arithmetical progrefEon, ) are not thofe that ftand at 
equal diftances on the QuadrantalArch extended,Fig. 6. 
39. But, ilandiug at unequal diftances (opt the fame 
extended Arch 5 ) Namely, on thofe points thereof, who's 
right Sines (whilft it was a Curve) are in Arithmetical 
Progreffion. As Fig. 8. 
40. To find therefore the. luagnitude' of \ELf^ 
Fig. 6^ Which is the fame with that of Fig. 8. (fup- 
pofing £ L of the fame length in both 5 however the 
number of Secants therein may be unequal:; we are to 
confider the Secants, though at unequal diftances, 
Fig. 8. to be the (ame with thofe at equal diftances in 
Fig. 7. anfwering to Sines in Arithmetical Progreffion. 
41. Now thefe Intervalls (or portions of the bafe) in 
Fig. 8. are the fame with the intercepted Arches (or 
portions of the Arch) in Fig. 7. For this Bafe is but 
that Arch extended. 
42. And thi'ie Arches Tin parts infinitely fmall) are 
to be reputed equivalent to the portions ot their re- 
fpcdive Tangents intercepted between the fame ordi- 
nates. As in Fig. 7.9. 43. That 
