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, Τόμος 1

University at Cambridge, 1801 - 426 σελίδες
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Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 170 - Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.

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