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a₁ added amount antilog arithmetical arrangements b₁ balls binomial called chance coefficients column common complete constant contains continued convergent cube Demonstration denominator determinant difference divided division divisor equal equation event evident EXERCISE exponent expressed Extract factors feet figures Find Find the value finite four fraction function geometrical Given greater hence Illustration increases infinite integer interest less limit logarithm means method miles Multiply negative Note obtained origin places positive powers Principles Problem progression proportion prove quadratic quantity quotient ratio Reduce remainder represent Required root Show Solution Solve square square root Substitute Subtract Take taken things third tion true units unknown quantities variable varies vector whence
Page 57 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 254 - For, since 10" = 10, the log. of 10 is 1 ; and since 10° = 1, the logarithm of 1 is 0. PRIN. 3. — The characteristic of the logarithm of a decimal is negative, and is numerically one greater than the number of ciphers between the decimal point and the first significant figure. For, if we raise the base, 10, to powers which give decimals, we will have, 10° = 1 ; hence, log 1 = 0 ; 10—'=.
Page 39 - ... term is found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place.
Page 38 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the two, plus the square of the second.
Page 239 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 8 - Magnitudes which are equal to the same magnitude, or equal magnitudes, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal...
Page 302 - A MORTGAGE is the conveyance of an estate, by way of pledge for the security of debt; and to become void on payment of it.
Page 202 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.
Page 8 - AXIOMS. 1. Things that are equal to the same thing are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are equal. 6. Equal powers of equal quantities are equal.