## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

### From inside the book

Results 1-5 of 32

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**remainder**after subtracting b from a . 4. The sign X is called the sign of multiplication , and placed between two quantities denotes that they are to be multiplied together . A point is often used instead of this sign , or , when the ... Page 8

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**remainder**C - A is as much too small as the quantity subtracted is too large , that is , as much as A is larger than A - B. The required re- mainder is , consequently , obtained by increasing C - A by the excess of A above A - B , that ... Page 18

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**remainder**must be equal to the sum of the products of the divisor by the remaining terms of the quotient , and may be used as a new dividend to obtain another term of the quotient . By pursuing this process until the dividend is ... Page 19

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**remainder**from which it is obtained , and is subtracted from this dividend or**remainder**. 64 x6 - 16 a3 x3 + a6 4x2 - 4 a x + a2 = Divisor . 64 x6-64 a x5 + 16a2x4 / 16x4 + 16ax3 + 12 a2x2 + 4a3x + a4 64 α χ5 - 16 α2 x4 - 16 a3 x3 + ... Page 22

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**remainder**, as follows . an ζη a - b an - an - 1 ban - 1 1st**Remainder**= an - 1b - b2 = b ( an - 1 - bn - 1 ) . Now , if the factor an - 1 - fn - 1 of this**remainder**is di- visible by a - b , the**remainder**itself is divisible by a ...### Other editions - View all

### Common terms and phrases

126 become zero 3d root arithmetical mean arithmetical progression Binomial Theorem coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence