## The first principles of algebra, for the use of the boys of the Royal hospital schools, Greenwich1845 |

### From inside the book

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**Divide**each term of the dividend by the divisor , and connect each quotient with its proper sign . EXAMPLES . 14xy - 16xy divided by 2xy , or 14x2y3 — 16x3y = 7xy2 — 8x3 . 2xy 14ab3c - 9a3bc3 — 6a2b3c2 : 463 - 3a2c2 - 2abc 3abc 25x3y3z3 ... Page 29

... the dividend , leaves -xy . Bringing down + y the operation is resumed as before . EXAMPLES .

... the dividend , leaves -xy . Bringing down + y the operation is resumed as before . EXAMPLES .

**Divide**x2 + 3xy + 2y2 by x + y . x + y ) x2 + 3xy + 2y2 ( x + 2y x2 + xy 2xy + 2y 2xy + 2y3**Divide**6x2 + 5x - 6 by 3x - 2 c 3 DIVISION . 29. Page 30

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**Divide**x - y by x + y . x + y ) x - y2 ( x - y x2 + xy -xy - y * -xy - y3**Divide**x3 - 1 by x - 1 . x - 1 ) x3 - 1 ( x2 + x + 1 x3 - x2 x2 - 1 x2 -X x - 1 x - 1**Divide**122 + 6xy - 6y by 4x - 2y . 4x - 2y ) 12x2 + 6xy — 6y2 ( 3x + 3y 12x2 ... Page 31

Admiralty.

Admiralty.

**Divide**ax + ay - bx - by by a - b . a - b ) ax + ay - bx — by ( x + y ах - вх ay - by ay - by**Divide**x3 - mx3 + nx3 – mn by x2 . m . x2 — m ) x3 — mx3 + nx3 — mn ( x2 + n x3 - mx3 поха - тп nx2 - mn 3**Divide**24a3x * y * ——_ ... Page 32

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**Divide**1 by 1 + x . 1 + x ) 1 ( 1 1 + x remainder · · -X 1 х 1 1 + x 1 + x**Divide**y3 by y3— x2 . y2 - x2 ) y3 ( y y3 — x2y remainder + x2y y3 x2y y2 - x2 ・= y + ⋅ y2 - x2 EXAMPLES IN DIVISION . 1 .**Divide**4ax by 2ax Ans . 2x 2.**Divide**...### Common terms and phrases

1st equation 2nd equation a+b+c a²+b² algebraical algebraical quantities apples arithmetical progression ax³ boys coefficient common arithmetic common denominator common difference contained cube root Diff Divide dividend and divisor division equa equal Extract the square farthing Find 2 numbers find the numbers Find the sum Find the value frac fractions geometrical progression given equations gression known last example last term least common multiple left hand term letters lowest terms means minator Mult multiplicand negative quantity nth root number of terms numerator and denominator placed positive quantity quadratic equation quantities are proportionals question quotient ratio Reduce remainder represented ROYAL HOSPITAL SCHOOLS Rule signifies SIMPLE EQUATIONS simple form square root substituting subtracted surd taken tion tities unity unknown quantities Vulgar Fractions x²y ах х х ха

### Popular passages

Page 116 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.

Page 91 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.

Page 118 - If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents.

Page 91 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.

Page 23 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 23 - The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second.

Page 23 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.

Page 1 - The Sign of Subtraction, — , is read minus. It denotes that the quantity to which it is prefixed is to be subtracted. Thus, a — b, denotes that b is to be subtracted from a.

Page 128 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.

Page 62 - First, if necessary, clear of fractions ; then transpose all the terms containing the unknown quantity to one side of the equation, and the known quantities to the other.