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

### From inside the book

Results 1-5 of 23

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**sign**before it , the**sign**+ is always understood ; thus , 3a2b is the same as + 3a2b , and 5a - 3b is the same as + ...**square root**of a2 is a ; because a Xa = a2 , the**square root**of 25 is 5 ; the cube root of 27 = 3 ; the fourth ... Page 6

... square root of 3 , 5 , 7 , & c .; t cube root of 7 , 9 , & c . 18. The roots of quantities are expressed means of the

... square root of 3 , 5 , 7 , & c .; t cube root of 7 , 9 , & c . 18. The roots of quantities are expressed means of the

**radical sign**✓ , with the proper i dex annexed , or by fractional indices placed at th right - hand of the quantity ... Page 316

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**square root**of a2 = a or -a ; for + ax + a = + a2 , and -ax - a = + a2 . In fact , the 2mth root of arm is equal to + a or or -a ; for ( a ) 2m = ( a ) × am = a2m ( Art . 280 ) . 296. Any odd root of a**sign**as the quantity itself . root ... Page 334

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**radical sign**is used , which is nothing else but the initial of the word root , deformed , it is placed over the power , and in the opening of which the in- dexm of the root to be extracted is written . P We have therefore " a = am ... Page 335

... square root , the sign is used without the index 2 ; thus , the square root of ar is written Var , as has been already observed , ( Art . 18 ) . Quantities having the

... square root , the sign is used without the index 2 ; thus , the square root of ar is written Var , as has been already observed , ( Art . 18 ) . Quantities having the

**radical sign**v prefixed to them , are called radical Quantities ...### 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...