# 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

University at Cambridge, 1801 - Mathematics - 426 pages

### Contents

 EXPLANATION of Characters Page 9 Reduction 36 Compound Addition 43 DUODECIMALS 56 Reduction of Vulgar Fractions 63 Addition of do 72 Addition of Decimals 78 Reduction of do 85
 Simple Interest 182 Insurance 188 Equation of Payments 195 Compound Interest 202 Annuities at Simple Interest 209 ALGEBRA 263 Addition 269 Multiplication 277

 CIRCULATING DECIMALS 93 Addition of do 99 Simple Proportion or Rule of Three 105 Practice 118 Compound Proportion 125 Barter 131 Double do 137 Involution 147 Extraction of the Square Root 155 Arithmetical Progression 168 Geometrical do 175
 Fractions 289 Involution 308 Sards 326 Simple Equations 333 Reduction of two three or more Simple Equations to one 339 Quadratic Equations 354 Cubic and Higher Equations 370 GEOMETRY 381 Problems 392 Construction of the Plane Scale Prob L 420

### Popular passages

Page 352 - 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 54 - 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 136 - 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 379 - 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 166 - 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 127 - ... 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 350 - 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 388 - 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 244 - 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 168 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.