## Mathematics: Compiled from the Best Authors and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volume 1 |

### From inside the book

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Page 358

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**completing the square**. 72 Thus , x + ax = b , or x + ax = b , are the same as quadratics , and the value of the unknown quantity may be determined accordingly . EXAMPLES . have x = + b + for the affirmative value of x , and 4 a a 4 a ... Page 359

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**completing the square**; Then √x + 4x + 4 = 144 by extracting the root ; Or x + 2 = 12 , And therefore X12-2 = 10 . 2. Given x2 - 6x + 8 = 80 ; to find x . First , x2 - 6x = 80-8 = 72 by transposition ; Then x2 - 6x + 9 = 72 + 9 = 81 by ... Page 360

... completing + by evolution ; 4a 2 dc 62 + 2 4a a 8. Given x2 + 2ax2 = b ; to find x . Here , x2 + 2ax2 + ab + a * by

... completing + by evolution ; 4a 2 dc 62 + 2 4a a 8. Given x2 + 2ax2 = b ; to find x . Here , x2 + 2ax2 + ab + a * by

**completing the square**, 2 2 And x2 + ab + a " by evolution Whence x2 = √b + a - a , And consequently x = √ √bta : 9 ... Page 361

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**square**, a And x 11 62 4a2 b 24 2 = b a c - d a + 62 1 4a2 by**completing**the c - d 62 a + 4 by evolution ; c - d 44 2 Therefore + 2a ± √ And consequently x =土 2a a 62 4a2 c - d 62 + 4a2 a 2 EXAMPLES FOR PRACTICE , 1. Given x2 - 8x + ... Page 362

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**completing the square**; Also x + 4 = 256 = 16 by evolution ; And therefore x = 16-4 = 12 = less number , and 12-18 20 greater . 2. To divide the number 60 into two such parts , that their product may be 864 . Let x = greater part , Then ...### Contents

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### Common terms and phrases

2qrs amount angle annuity annum arithmetical bushel called carats cent centre circle circumference coefficient common denominator completing the square compound interest cube root cyphers decimal denoted discount Divide dividend division divisor draw equal equation EXAMPLES exponent farthings figures find the value fourth gallons geometrical progression geometrical series give given Line given number greater greatest common measure improper fraction integers least common multiple less number logarithm manner multiplicand Multiply negative NOTE nth root number of combinations number of terms number of things payment perpendicular pound present worth PROBLEM PROBLEM proportion quotient radius ratio Reduce remainder repetend required to find shews shillings sides simple interest square root subtract Suppose surd taken tare third triangle TROY WEIGHT unknown quantity vulgar fraction Whence whole number yards

### Popular passages

Page 354 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Page 56 - In the same manner multiply all the multiplicand by the inches, or second denomination, in the multiplier) and set the result of each term one place removed to the right 'hand of those in the multiplicand.

Page 138 - As the sum of the several products, Is to the whole gain or loss : So is each man's particular product, To his particular share of the gain or low. EXAMPLES. 1. A, B and C hold a pasture in common, for which they pay 197.

Page 381 - A point is a dimensionless figure ; or an indivisible part of space. A line is a point continued, and a figure of one capacity, namely, length. A superficies is a figure of two dimensions, namely, length and breadth. A solid is a figure of three dimensions, namely, length, breadth, and thickness.

Page 168 - The first term, the last term, and the number of terms given, to find the sum of all the terms. RULE.* — Multiply the sum of the extremes by the number of terms, and half the product will be the answer.

Page 129 - ... have to their consequents, the proportion between the first antecedent and the last consequent is discovered, as well as the proportion between the others in their several respects.

Page 352 - B's, and B's is triple of C's, and the sum of all their ages is 140. What is the age of each ? Ans. A's =84, B's =42, and C's =14.

Page 389 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.

Page 246 - Briggs' logarithm of the number N ; so that the common logarithm of any number 10" or N is n, the index of that power of 10 which is equal to the said number. Thus, 100, being the second power of 10, will have 2 for its logarithm ; and 1000, being the third power of 10, will have 3 for its logarithm. Hence, also, if 50 = 101-00*7, then is 1.69897 the common logarithm of 50.

Page 170 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.