Elements of algebra, compiled from Garnier's French translation of L. Euler. To which are added, solutions of several miscellaneous problems1824 |
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Resultat 1-5 av 56
Side 12
... divided is called the dividend ; the number of equal parts sought is called the divisor ; the magnitude of one of these parts is called the quotient . Thus in the foregoing example , 12 is the dividend , 3 is the divisor , 4 is the ...
... divided is called the dividend ; the number of equal parts sought is called the divisor ; the magnitude of one of these parts is called the quotient . Thus in the foregoing example , 12 is the dividend , 3 is the divisor , 4 is the ...
Side 13
... divided by 7 , we must seek such a product as , taking 7 for one of its factors , the other factor multiplied by it ... divided by b , the quotient will be a . And in general in all the instances of division , if the divi- dend be ...
... divided by 7 , we must seek such a product as , taking 7 for one of its factors , the other factor multiplied by it ... divided by b , the quotient will be a . And in general in all the instances of division , if the divi- dend be ...
Side 14
... divided by + a , the quo- + tient will be evidently +6 . But if it be proposed to divide + ab by a the quotient will be -b , because a multiplied by - b gives + ab . If the dividend be - ab , and it is pro- - posed posed to divide it by ...
... divided by + a , the quo- + tient will be evidently +6 . But if it be proposed to divide + ab by a the quotient will be -b , because a multiplied by - b gives + ab . If the dividend be - ab , and it is pro- - posed posed to divide it by ...
Side 15
... divided by -3p , the quotient will be -6q ; also - 30xy divided by + 6y gives - 5 x ; and - 54 abc by -96 gives + 6ac . OF THE DIFFERENT METHODS OF CALCULATING COMPOUND QUANTITIES . CHAP DIVISION OF SIMPLE QUANTITIES . 15.
... divided by -3p , the quotient will be -6q ; also - 30xy divided by + 6y gives - 5 x ; and - 54 abc by -96 gives + 6ac . OF THE DIFFERENT METHODS OF CALCULATING COMPOUND QUANTITIES . CHAP DIVISION OF SIMPLE QUANTITIES . 15.
Side 24
... divided , we obtain the following Theorem , presenting an algebraical proof of Euclid's Prop . IV . Book II . , viz . , that If a number be divided into any two parts , the square of the whole number is equal to the squares of the two ...
... divided , we obtain the following Theorem , presenting an algebraical proof of Euclid's Prop . IV . Book II . , viz . , that If a number be divided into any two parts , the square of the whole number is equal to the squares of the two ...
Innhold
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Vanlige uttrykk og setninger
already seen arithmetic means arithmetic series arithmetical progression assume binomial cent CHAP coefficient common difference Completing the square consequently consider contains cube root decimal determine divided dividend divisible equal equation evident example exponent expressed Extracting the root factors find the greatest Find the sum find the values formula four roots fourth term geometric means geometrical progression given number gives greater number greatest common divisor greatest common measure Hence infinite series infinitum instance integer irrational last term less letters logarithm manner method multiplied negative numbers number of permutations number of terms obtain quadratic surds quotient radical sign ratio reduced remainder represented required to find rule second degree second term square root subtracted suppose third degree three numbers tion transposition unity unknown quantity whence whole number
Populære avsnitt
Side 46 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Side 24 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 228 - There are three numbers in geometrical progression ; the sum of the first and second of which is 9, and the sum of the first and third is 15.
Side 36 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Side 248 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Side 58 - We call this new species of numbers, irrational numbers ; they occur whenever we endeavour to find the square root of a number which is not a square. Thus, 2 not being a perfect square, the square root of 2, or the number which, multiplied by itself, would produce 2, is an irrational quantity. These numbers are also called surd quantities, or incommensurables.
Side 243 - Find two numbers, such, that their sum, their product, and the difference of their squares shall be all equal to each other.
Side 77 - any quantity may be transferred from "one side of the equation to the other, by changing its sign ;" and and it is founded upon the axiom, that " if equals be added to " or subtracted from equals, the sums or remainders will be
Side 113 - Ans. 3 and 7 8. The difference of two numbers is 2, and the difference of their cubes is 98; required the numbers. Ans. 5 and 3 9.
Side 37 - If the numerator and denominator are both, multiplied or both divided by the same number, the value of the fraction will not be altered.