# 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

 FEDERAL MONEY 90 Addition of 99 Simple Proportion or Rule of Three 105 Practice 118 Compound Proportion 125 Conjoined 131 Alligation Medial 140 Extraction of the Square Root 152 Cube Root by Approximation 160 Arithmetical Progression 168 Geometrical 182 Equation 195 Compound Interest 202 Annuities at Simple Interest 209
 Multiplication 277 Division 285 Fractions 294 Involution 308 Surds 316 Infinite Series a 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 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.