## An Elementary Treatise on Algebra: Theoretical and Practical |

### From inside the book

Results 1-5 of 32

Page 46

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**divi**- dend without altering the quotient , and the division is reduced to that of , which admits of no farther m reduction without assigning numeral values to c and m . 35. If all the terms of a compound quantity be divided by a simple ... Page 49

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**divi**- sion of am by a " , or by am + d = am Xad ; by suppress- ing the factor a " , which is common to the dividend and divisor , according to what has been demonstra- ted with regard to the division of letters ( Art . 84 ) , 1 ad we ... Page 51

... and dividend are both simple quan- tities . RULE . 91. Divide , at first , the coefficient of the

... and dividend are both simple quan- tities . RULE . 91. Divide , at first , the coefficient of the

**divi**- dend by that of the divisor ; next , to the quotient annex those letters or factors of the dividend that are DIVISION . 51. Page 52

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**divi**- dend , and the remainder is the exponent of that letter in the quotient . EXAMPLE 1. Divide 18ax2 by 3ах . 18αχ2 18 Зах 18ax2 3 18 Or , Зах 3 ( Art , 86 ) . 22 X - X = 6 × 1 × x2 - 1 = 6x . α a --1 30 Xa1 Xa24 = 6Xa ° × x = 6x ... Page 53

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**divi**- sor , divides exactly that of the dividend . When these conditions do not take place , then , after cancelling the letters , or factors , that are com- mon to the dividend and divisor ; the quotient is expressed , in the manner of ...### Other editions - View all

### Common terms and phrases

a²-b² a²+ab+b² a²+b² according added algebraic quantities ax+by=c becomes changing the signs coefficients common denominator completing the square compound quantity consequently cube root deduce difference divi Divide dividend division enunciation equa equal example exponent expressed factor Find the greatest find the values formula frac fraction required give greater greatest common divisor greatest common measure Hence improper fraction infinite series infinity involving least common multiple letter lowest terms lues manner method miles mixed quantity numbers or quantities observed operation preceding prefixed Prob problem proper sign proposed equations quotient radical sign reciprocal Reduce remainder Required the product required to find result RULE second equation shillings side simple equations simple quantity square root subtracted surd three equations tion tity transposition unity unknown quantities value of x whence whole number ах

### Popular passages

Page 491 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...

Page 241 - Find the value of one of the unknown quantities, in terms of the other and known quantities...

Page 320 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 325 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power...

Page 499 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.

Page 454 - There are four numbers in arithmetical progression : the sum of the squares of the two first is 34 ; and the sum of the squares of the two last is 130. What are the numbers?

Page 495 - Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third shall have the same ratio to the second and fourth...

Page 503 - IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth...

Page 287 - A cask, which held 146 gallons, was filled with a mixture of brandy, wine, and water. In it there were 15 gallons of wine more than there were of brandy, and as much water as both wine and brandy. What quantity was there of each...

Page 492 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth; then the first is said to have to the second a greater ratio than the third...