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let a now reprefent the middle Ordinate, and the Area 
fliall be equal a+ ~ -f x ~- — h &c. 
And this is the Theorem which the Author makes 
mod Ufe of. When the feveral intermediate Or- 
dinates reprefent the Terms of a Progrellion, the 
Area is computed from their Sum, or converfely their 
Sum is derived from the Area, by Theorems that eafily 
flow from thefe. 
Thefe general Theorems are afterwards applied for 
finding the Sums of the Powers of any Terms in 
Arithmetical Progreffion, whether the Exponents of 
the Powers be Pofitive or Negative, and for finding 
the Sums of their Logarithm, and thereby determin- 
ing the Ratio of the Unci a of the middle Term of a 
Binomial of a very high Power to the Sum of all the 
Uncice. This laft Problem was celebrated amongft 
Mathematicians fome Years ago, and by endeavouring 
to refolve it by the Method of Fluxions the Author 
found thole Theorems, which give the fame Con- 
clufions that are derived from other Methods. They 
are likewife applied for computing Areas nearly from 
a few equidiftant Ordinates, and for interpolating 
the intermediate Terms of a Series, when the Na- 
ture of the Figure can be determined, whofe Ordi- 
nates are as the Differences of the Terms. 
In the laft Chapter, the general Rules, derived 
from the Method of Fluxions for the Refolution of 
Problems, are deferibed and illuftrated by Examples. 
After the common Theorems concerning Tangents, 
the Rules for determining the greateft and leaft Or- 
dinates, with the Points of contrary Flexure, and the 
Precautions that are necefiary to render them accurate 
and 
