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
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according added addition amount angle annuity answer bought called carried cent centre changes circle combinations common common denominator common measure compound consequently consist contained continually cube cyphers decimal DEMONSTRATION denominator describe difference Divide dividend division divisor draw equal equation equivalent evident EXAMPLES expressed extremes figures four fourth fraction gain gallons give given number greater greatest half hand interest least less letters logarithm manner Marked means method mixed months multiplicand Multiply nature negative NOTE operation payment pound PROBLEM Proof proportion quantity question quotient radius ratio reason Reduce remainder root RULE shillings sides simple single square root subtract Suppose taken things third true units weight whole write yards
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 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.