A Course of Mathematics in Two Volumes Composed And More Especially Designed

Cover A Course of Mathematics in Two Volumes Composed And More Especially Designed
A Course of Mathematics in Two Volumes Composed And More Especially Designed
Charles Hutton
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Find the cube root of -— ^ — ■ — ;7n in an infinite ferles.
Anf. -—X ( 1 — -— T + r r* &C4 * . Cix 1 1 . Find the value of — ^ -, in an infinite feries.
a~ — ax -{- . V . . X ^2 ^4 x^ ^ Ani. — + o r - -^> &c.
a or a> a^ ARITHMETICAL PROPORTION.
Arithmetical Proportion is the relation which two quantities, of the fame kind, bear to each otlier, in refped; to their difference.
Four quantities are faid to be in Arithmetical Proportion, when the difference between the firft and feCond is equal to t
...he difference between the third and fourth.
Thus, 3, 7, 12, 16, and a^ a -{- h, c, c -^ b, are arith- metically proportional.
Arithmetical Progrefiion is when a feries of quantities cither increale or decreafe by the iame common difference.
Thus, 1, 3, 5, 7, 9, 11, S^c, and a, a -{- b, a + 2b, a + 3^, a -\- 4:bf a -\-bb, &:c, are feries in arithmetical progrefiion, whofe common differences arc 2 and b.
The moft ufeful part of arithm. Etical proportion is con- tained in the following theorems : 1 .


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