[ iH ] 
continued to fuch a Number of double FaBors as are expreffed by a+i, 
or half the Index ? which in this cafe is an even Number. S 
2 ^ 
S+Ia (2a+I will be equal to n. nn— 4. nn- 16. nn- 36, and fo on 
where there are to be fomany double PaBors as with one fngle one (n) 
will make up the Index 2-a+i, which is an odd Number. 
If the common Difference ct be an Unit 3 it is omitted 
Thus , ^(6 is = n.n~T . n — 2. n— 3 . 5 ^ 4 - containing 6 Faftors , 
50 T( 6 « =5 6. 5. 4. 3. 2. 1, like for others. 
If the common Difference ct be nothing ? ^ <?77Z/ > 
and it becomes the fame with the Geometrical Power . 
o 1 
So n-£-a^ — - n — - 1 according to the common Notation. 
Proposition I. 
An Arch lets than, a Semicircle being given, with 
a Taint in the Thame ter faffing through one of 
rf iltr entities ; to find, by means of the Sine, 
o f a 'given Tart of the Arch left than one half , 
IheArea of the- Setter fubt ended by the givers 
Anh, and comprehended in the. Angle made at. 
the ffiveti *P olut • 
Let PN A be a Semicircle deferibed on the Centre 
c and Dieter AP, and let PN be the gt.en Arch 
k6 than a Semicircle, and S the given Point in thcDta- 
AP Da ffin^ thro’ one of the Extremities of the 
Amh NP hr P Then taking any Number » bigger 
than i, let PK be an 
Arch in Proportion to 
the given Arch PN, as 
Unity to the Number 
n ; and let it be required 
to find by means of the A 
