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Page 150 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 78 - If the number be divided by the sum of the digits, the quotient will be 26; but, if 198 be added to it, the digits will be inverted.
Page 70 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Page 55 - 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. A 14ff days, B 17ff, and C 23J y . 21.
Page 69 - This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in Prop.
Page 69 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Page 73 - Add all the extremes together and multiply their sum by half the number of terms, the product will be the sum of the series. Q. How do you find the sum of an arithmetical series ? EXAMPLES. 1. The extremes are 2 and 100, and the number of terms 22 : what is the sum of the series ? OPERATION.
Page 133 - Circumference of every circle is conceived to be divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. Degrees, minutes, and seconds, are denoted thus 25� 30
Page 158 - Hence, the area of a parallelogram is equal to the product of any two contiguous sides multiplied by the sine of the contained angle, radius being unity.
Page 26 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.