## A Treatise on Algebra |

### From inside the book

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**RATIO**AND PROPORTION . Definitions 214 ...... Properties of Proportions ....... 216 Variation ......... 222 Problems in Proportion ........ 224 CHAPTER XVI . PROGRESSIONS . Arithmetical Progression - General Principles ... Page 11

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**ratio**; c , circumference ; h , height , etc. All these letters may be used with accents . Thus , in , a problem relating to two circles , d may represent the diameter of one cir cle , and d ' the diameter of the other ; c the ... Page 15

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**ratio**consists of two points like the colon : placed between the quantities compared . Thus the**ratio**of a to b is written a : b . 22. The sign of proportion consists of a combination of the sign of**ratio**and the sign of equality , thus ... Page 94

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**ratio**of 5 to 12 . What was the share of each ? Beginners almost invariably put x to represent one of the quantities sought in a problem ; but a solution may often be very much simplified by pursuing a different method . Thus , in the ... Page 96

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**ratio**of 4 to 5. What sum must each receive ? Prob . 36. Divide the number a into three parts , which shall be to each other as m : n : p . Ans . ma na ρα ; m + n + p ' m + n + p ' m + n + p ' When p = 1 , Prob . 36 reduces to the same ...### Contents

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### Common terms and phrases

algebraic algebraic quantity arithmetical progression binomial binomial theorem cent Clearing of fractions coefficient common difference continued fraction cube root decimal denote digits diminished Divide the number dividend divisible dollars equa equal equation whose roots equations containing EXAMPLES exponent expression Extract the square factors figure Find the cube Find the fifth Find the fourth Find the number Find the square Find the sum find the values following RULE four fourth power fourth root geometrical progression greatest common divisor Hence indicates inequality infinite series last term least common multiple less logarithm monomial negative nth root number of terms obtain positive pounds preceding problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term simultaneous equations Solve the equation square root Sturm's Theorem suppose surd three numbers tion unity unknown quantity whence whole number zero

### Popular passages

Page 97 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...

Page 46 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 181 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons, and then, filling the vessel •with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.

Page 284 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.

Page 258 - We may obtain the sixth root by extracting the cube root of the square root, or the square root of the cube root. It is, however, best to extract the roots of the lowest degrees first, because the operation is less laborious. We may obtain the eighth root by extracting the square root three times successively.

Page 371 - ... force of attraction to vary directly as the quantity of matter, and inversely as the square of the distance, at what point between them will a third body be equally attracted by the earth and moon ? Ans.

Page 42 - Divide the coefficient of the dividend by the coefficient of the divisor.

Page 38 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.

Page 101 - RULE. Find an expression for the value of one of the unknown quantities in one of the equations, and substitute this value for the same unknown quantity in the other equation.

Page 139 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.