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arithmetical means arithmetical progression assume coefficient colog column common logarithms continued fraction convergent series decimal places denominator depressed equation determinant digits divergent series Dividing elements equal equation whose roots evidently EXERCISES expansion factor figure Find the value finite number following equations Form the equation formula geometrical means geometrical progression given equation given series graph harmonical mean Hence increases indefinitely infinite series integer last term limit logarithms mantissa of log method multiplying nth term number of combinations number of terms number of variations obtained order of differences partial fractions partial quotient periodic continued fraction permutations preceding article principle quadratic equation ratio real roots reciprocal equation recurring series result root of f(x second member series is convergent solution Solve the equation square pyramid Sturm's Theorem Substituting subtracted transformed equation unknown number variable variations of sign whence wherein yards
Page 415 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 351 - We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike.
Page 313 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Page 317 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 310 - Two workmen can do a piece of work in 6 days. How long will it take each of them to do the work, if it takes one 5 days longer than the other ? 19.
Page 360 - V(a2 — °^)> etc-, are functions of x ; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Page 315 - In any proportion the terms are in proportion by. Composition ; that is, the sum of the first two terms is to the first term, as the sum of the last two terms is to the third ter.n.
Page 323 - If a body falls 256 feet in 4 seconds, how far will it fall in 10 seconds?