[ 1200 3 
we are to interpret S, fuccefEvely, by i S,iS,3 S, &c» 
ti l we come to S, the greateft. Which therefore re- 
prelents the number of All. 
5-2. And becaufe the firft member doth reprefent a 
Series of Equals ; thefecond, of Secundans,* the third, 
of Quartans, &c. Therefore the firft member is to be 
multiplied, by S; the fecond, byJSi the third, by 
i Sj the fourth, by ^ S; Sec. 
/3. Which makes the Aggregate, 
S4|S^ 4[S^ 4iS^ 4lS^ &c. =ECLM, Fig. 9- 
/4, This ("becaufe S is allways lefs thanR= 1) may 
be fo far continued, till fome power of S become fo 
Imall as that it (and all which follow it^ may be fafely 
neglected. 
ff. Now (to fit this to the Sea-Chart, according to 
Latitude) given,' we are to find (by the Trigonometri- 
cal Canon j the Sine of fuch Latitude; and take, equal 
to it, e L = S. And, by this, find the magnitude ot 
EC LM, Fig. 9 ; that is, of R E L/, Fig. 8. that is, 
of R EL /, Fig, 6. And then , As R R LE (^or fb 
many times the Radius,; to R EL/ (the Aggregate of 
alL the Secants ; ) fo muft be a like Arch of the Equa- 
tor (equal to the Latitude propofed,) to the diftance oif 
fuch Parallel, (reprefenting the Latitude in the Chart) 
from the Equator. Which is the thing required. 
fd. The?' lame may be obtained, in like manner, by 
taking the Verfed Sines in Arithmetical progreffion. 
For if the right Sines (as herej beginning at the Equa- 
tor, be in ^r/>^;?2^^/V^/ progreffion, as i, 2, 3, 6cc. Then 
will the Verfed Sines, beginning at the Pole, fas be^ 
ing their complements to the Radius) be fo alfo. 
The Colleilion of Tangents^ 
f7. The fame may be applyed: in like manner, 
fthough that be not the prefent bufinefs,) to the Aggre- 
gate of TangentSj ("anfwering to the Arch divided mro 
Having the propofed Parallel (ot 
eq^al parts.}, 
j8;. For^ 
