# 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

W. Hilliard, 1808 - Mathematics
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### Contents

 ARITHMETIC 9 FEDERAL MONEY 17 Reduction 34 Compound Addition 40 CIRCULATING DECIMALS 69 PROPORTION IN GENERAL 95 42 109 Practice 110
 Miscellaneous Questions 208 LOGARITHMS 216 Description and Use of the Table of Logarithms 222 Division by 228 Addition 237 Multiplication 244 Division 251 Involution 273

 DUODECIMALS 119 Conjoined 121 Involution 133 Extraction of the Square Root 140 VULGAR FRACTIONS 141 Arithmetical Progression 151 Geometrical 164 Discount 170 Equation of Payments 175 Compound Interest 181 Annuities at Simple Interest 187 Value of an Annuity in Reversion at Compound Interest 193 Reduction of Vulgar Fractions 194
 Surds 280 Infinite Series 289 Simple Equations 295 Reduction of two three or more Simple Equations to one 301 Quadratic Equations 316 Cubic and Higher Equations 330 GEOMETRY 339 Problems 349 Construction of the Plane Scale Prob L 380 PLANE TRIGONOMETRY 387 DECIMAL FRACTIONS 397 MENSURATION OF SUPERFICIES 407 Problems relating 436

### Popular passages

Page 175 - RULE.* — Multiply each payment by the time at which it is due; then divide the sum of the products by the sum of the payments, and the quotient will be the true time required.
Page 140 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 255 - 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 198 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive \$ '75, and, for every day he was idle, he should forfeit \$ '25 ; at the expiration of the time, he received \$ 27'50 ; how many days did he work...
Page 149 - To the remainder bring down the first figure in the next period, and call it the dividend. 4. Involve the root to the next inferior power to that which is given, and multiply it by the number denoting the given power, for a divisor.
Page 313 - 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 124 - 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 loss.
Page 139 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 120 - When it is required to find how many of the first sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the last.
Page 132 - When one of the ingredients is limited to a certain quantity. RULE. Take the difference between each price and the mean rate, as before ; then,