Algebra, for High Schools and CollegesJ.S Cushing & Company, 1897 - 226 σελίδες |
Άλλες εκδόσεις - Προβολή όλων
Algebra for High Schools and Colleges (Classic Reprint) Ellen Hayes Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ absolute term algebraic function analytic geometry arithmetic arithmetic mean arithmetic series ax² b₁ b₂ binomial binomial theorem CHAPTER coefficient common logarithms constant contain deductive reasoning derivative determinant divided dividend divisor elementary algebra equa equal roots equation f(x equation f(x)=0 evaluated exactly divisible example expres Find the value finite follows formula fractional exponents geometry graph hence imaginary roots indicated inequality linear loga logarithms mathematics means monomial negative quantity nth degree number of roses odd number operation polynomial positive quantity preceding article proper fraction proposition quadratic quan quotient rational integral function real roots remainder represent result root of f(x second member sion student Sturm's theorem Sturmian functions subtracted Suppose surd symbol theorem tion unity unknown quantities vanish variable variation write α₁ α₂
Δημοφιλή αποσπάσματα
Σελίδα 80 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Σελίδα 25 - Two things may be observed on this comparison, First, how very much the shorthand expression gains in clearness from its brevity. Secondly, that it is only shorthand for something which is just straightforward common sense and nothing else. We may always depend upon it that algebra, which cannot be translated into good English and sound common sense is bad algebra.
Σελίδα 138 - An infinite series is said to be divergent when the sum of the first n terms can be made numerically greater than any finite quantity by taking n sufficiently great.
Σελίδα 101 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Σελίδα 198 - The logarithm of the product of two quantities is equal to the sum of the logarithms of the two quantities. Let p and q be the two ' quantities, and suppose m = log p and n = log q, the base being a. Then am = p and a" = q; therefore pq = ama" = a™+" ; hence loga (pq) = m + n ; 4.
Σελίδα 33 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 210 - The characteristic of the logarithm of a number greater than 1 is positive and is one less than the number of integral places in the number. For example, log 75 = 1 + some mantissa, log 472.8 = 2 + some mantissa, and log 14,800.75 - 4 + some mantissa.
Σελίδα 210 - The integral part is called the characteristic, and the decimal part the mantissa.
Σελίδα 134 - TJie coefficient of any term after the second is obtained by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing the product by a number greater by 1 than the exponent of b in that term.
Σελίδα 167 - Every equation of an even degree, whose last term is negative, has at least two real roots, one positive and the other negative.