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. . . . c. Y.Y. & cases, where a different mode # preseedfug appeared to be necessary, it has been chiefly compiled: great care having been taken, at the same time, to adapt it, as much as possible, to the wants of learners,and she general purposes *os in-fryction, agreeably to the design with *:: § #. #.. - g With this view, as well as in compliance with the wishes of several intessent teachers, I have, also, been led to subjoin to it, by way of an Appendix, a small tract on the application of Algebra to the solution of Geometrical Problems; which, it is hoped, will prove acceptable to such classes of students as may not have an opportunity of consulting more

voluminous and o: works on this interesting branch of theoscience.

JoHN BonnycASTLE.

Roy Al Military Academy,
Woolwich,
October 22, 1815.

xiv -Page Of the Binomial Theorem.......... “...... .o................ 143 Of the indeterminate Analysis................................. 150

162

Of the Diophantine Analysis................................... 173

Of the Summation and Interpolation of Series..........
Of Logarithms...................................... “............ 200
Multiplication by Logarithms.................................. 213
Division by Logarithms.......................................... 216
The Rule of Three by Logarithms......................... 218
Involution, by Logarithms....................................... 221
Evolution, by Logarithms....................................... 223
A Collection of Miscellaneous Questions.................. 226
Appendix, on the application of Algebra to Geometry 233

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ALG EBRA,

- - N _-e - – Algebra is the science which treats of a general method of performing calculations, and resolving mathematical problems, by means of the letters of the alphabet. Its leading rules are the same as those of arithmetic ; and the operations to be performed are denoted by the following characters ; + plus, or more, the sign of addition; signifying that the quantities between which it is placed are to be added

together. •r| Thus, a-Hb shows that &mber, or quantity, represented by b, is to be added to that represented by a ;

and is read a plus b.
minus, or less, the sign of subtraction; signifying
that the latter of the two quantities between which it is
placed is to be takeofoom the former. **
Thus a–b shows that the quantity represented b
is to be taken from that represented by a ; and is readba
minus b
Also, a,b represents the difference of the two quan-
tities a and b, when it is not known which of them is the
greater -
X into, the sign of multiplication; signifying that the
quantities between which it is placed are to be multiplied
together. ---- ***

--

--> ... ----e.

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Thus, a Xb shows that the quantit is to be multiplied by that represente a into b.

d by & and is read

The multiplication of simple quantities is also frequently denoted by a point, or by joining the letters together in the form of a word.

Thus, a Xb, a , b, and ab, all signify the product of a and b : also, 3Xa, or 3a, is the product of 3 and a ; and is read 3 times a.

-- by, the sign of division ; signifying that the former of the two quantities betwe hich it is placed is to be divided by the latter. woulso -

Thus, a-i-b shows that the quantity represented by a is to be divided by that represented by b : and is read a by b, or a divided by b.

Division is also frequently denoted by placing one of

the two quantities over the other, in the form of a fraction. *

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vided by a ; and #* that a-b is to be divided by a-Fc.

= equal to, the sign of equality ; signifying that the quantities between which it is placed are equal to each other.

Thus, z=a + b shows that the quantity denoted by 2: i al to the sum of the quantities a and b; and is read acUsual to a plus b.

*= identical to, or the sign of equivalence ; signifying that the expressions between which it is placed are of the same value, for all values of the letters of which they are composed.

Thus, (x+a) × (z—a) =z”—a”, whatever numeral values may be given to the quantities represented by a

and a. T--> __-

* *-* . ) •

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