## The student's algebra |

### From inside the book

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**axioms**deduced from Euclid's Elements . 1. If equal quantities be added to equal quan- ties , their sums will be equal . 2. If equal quantities be subtracted from equal quantities , their remainders will be equal.— Cor . Hence , if the ... Page 34

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**axiom**2 ) , 3x = 21 ; and (**axiom**4 ) , x = 7 . Also , if 3x + 4 = a + x ; then by transposition 3x- a + x x = a — 4 , or 2x = a - 4 ; ... (**axiom**4 ) x = ~ 2 1 Also , if 3x - 4 = 2x + 3 , then by transposition , 3x - 2x = 3 + 4 , or x ... Page 35

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**axiom**4 ) , x == 4a 5 8. If every term in an equation be multiplied by any number , the equation will retain its equality , (**axiom**3 ) . Thus , if 3x + 4 = 16 , multiply the whole by x , and it becomes 3x2 + 4x = 16x . • 9. If every ... Page 43

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**Axiom**4 ) , x = - - = 4 . Or thus , ( 6 ) by transposition , 3x - 2x - 6x = -13-7 . ... By Addition , -5x = -20 ; then ( 6. Cor . ) , 5x = 20 ; . ' . ( ax . 4 ) x = - 20 5 3. Given 3a + 4x = 2b - x , to find the value of x . Here ( 6 ) ... Page 44

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**Axiom**4 , ) x = - 3x 20 = 4 . 5. Given 4x + = + 16 , to find the value of x . 5 3 Here ( 10 ) , multiplying the equation by 15 , the least common multiple of 5 and 3 , 60x + 3x = 15x +240 ; .. ( 6. ) by transposition , 60x + 3x - 15x ...### Common terms and phrases

5th power added Algebra Algebraist answer the conditions arithmetical progression axiom bushels coefficient completing the square compound quantity cube root denominator difference digits dividend divisor equa EXAMPLES FOR PRACTICE extracting the root extracting the square find the values Find two numbers four numbers four quantities fourth power gained gallons geometrical progression given equation hence least common multiple lues miles multiplying this equation number of yards Pure Quadratics QUADRATIC EQUATIONS quan quantities be proportionals question quired quotient radical sign ratio remainder Required each person's Required the cube Required the length Required the number Required the price Required the sides Required the square second equation second term shillings Simple Equations simple quantity sold solution square root squaring each side substituting this value subtracted surd quantity Theorem third three numbers transposing transposition unknown quantity values of x vulgar fraction whence whole number yards of silk

### Popular passages

Page 13 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 11 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.

Page 14 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.

Page 79 - Prob. 3. Find two numbers, the greater of which shall be to the less, as their sum to 42 ; and as their difference to 6.

Page 13 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth...

Page 40 - Sib., his head weighs as much as his tail and half his body, and his body weighs as much as his head and his tail ; what is the whole weight of the fish ? . Aas.

Page 13 - In any proportion, the product of the means is equal to the product of the extremes.

Page 13 - Composition, when the sum of the first and second is to the second as the sum of...

Page 80 - A farmer with 28 bushels of barley at 2s. 4d. per bushel, would mix rye at 3 shillings per bushel, and wheat at 4 shillings per bushel, so that the whole mixture may consist of 100 bushels, and be worth 3s. 4d. per bushel. How many bushels of rye, and how many of wheat must he mix with the barley ? Ans.