The Elements of Algebra: Designed for the Use of Students in the UniversityJ. Smith, 1815 - 305 σελίδες |
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Σελίδα 103
... varying and dependent quantities bear to each other , the conclusions are more readily obtained , by ex- pressing only ... vary directly as another , when the two quantities depend wholly upon each other , and in such a manner , that if ...
... varying and dependent quantities bear to each other , the conclusions are more readily obtained , by ex- pressing only ... vary directly as another , when the two quantities depend wholly upon each other , and in such a manner , that if ...
Σελίδα 104
... vary directly as B. Ex . If the altitude of a triangle be invariable , the area varies as the base . For if the base be increased , or diminished , the area is increased or diminished in the same proportion * . ( 194. ) DEF . 2. One ...
... vary directly as B. Ex . If the altitude of a triangle be invariable , the area varies as the base . For if the base be increased , or diminished , the area is increased or diminished in the same proportion * . ( 194. ) DEF . 2. One ...
Σελίδα 105
... vary as a second , and that second as a third , the first varies as the third . Let A a B : b , and B : b :: C : c , then , ( Art . 176 ) , A : a :: C : c . That is , Ax C. In the same manner , if A∞ B and B∞ , then A. 1 C ( 198. ) If ...
... vary as a second , and that second as a third , the first varies as the third . Let A a B : b , and B : b :: C : c , then , ( Art . 176 ) , A : a :: C : c . That is , Ax C. In the same manner , if A∞ B and B∞ , then A. 1 C ( 198. ) If ...
Σελίδα 106
... vary as the third . Let A Cand Boc C , then A + Boc C ; also , AB : C. By the supposition , A : a :: C : c : B : b ... vary as another , it will also vary as any multiple , or part , of the other . Let Acc B , and m be any constant ...
... vary as the third . Let A Cand Boc C , then A + Boc C ; also , AB : C. By the supposition , A : a :: C : c : B : b ... vary as another , it will also vary as any multiple , or part , of the other . Let Acc B , and m be any constant ...
Σελίδα 107
... vary as another , any power or root of the former will vary as the same power or root of the latter . Let A vary as B , then A : a :: B : b , and by Art . 188 , A " : a " :: B " : b " ; that is , Aoc B " , where n is whole or fractional ...
... vary as another , any power or root of the former will vary as the same power or root of the latter . Let A vary as B , then A : a :: B : b , and by Art . 188 , A " : a " :: B " : b " ; that is , Aoc B " , where n is whole or fractional ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
abscissa algebraical quantities annuity arithmetical progression assumed binomial biquadratic coefficients common denominator conic section cube root cubic equation curve decimal Diff difference divided dividend division divisor equa equal expressed factors find the sum former fraction geometrical progression greater greatest common measure greatest root hence impossible roots increment integral last term least common multiple less Let the roots limiting equation logarithm m.m+r m+r.m+2r manner multiplied negative roots nth term numerator and denominator obtained odd number ordinates original equation parabola positive possible roots present value probability proportionals proposed equation quadratic surds quan quotient ratio reduced remainder represented shillings signs simple equation square root substituted subtracted suppose supposition taken tion tities unity unknown quantity vulgar fraction whole number
Δημοφιλή αποσπάσματα
Σελίδα 64 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.
Σελίδα 44 - Divide this quantity, omitting the last figure, by twice the part of the root already found, and annex the result to the root and also to the divisor, then multiply the divisor as it now stands by the part of the root last obtained for the subtrahend.
Σελίδα 52 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 37 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 73 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Σελίδα 44 - Divide the number thus formed, omitting the last figure, by twice the part of the root already obtained, and annex the result to the root and also to the divisor. Then multiply the divisor, as it now stands, by the part of the root last obtained, and subtract the product from the number formed, as above mentioned, by the first remainder and second period. If there be more periods- to be brought down, the operation must be repeated.
Σελίδα 13 - Multiply as in whole numbers, and point off as many decimal places in the product as there are in both multiplicand and multiplier. DIVISION. Divide as in whole numbers, and point off...
Σελίδα 73 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Σελίδα 73 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 50 - Let the equation first be cleared of fractions ; then transpose all the terms which involve the unknown quantity to one side of the equation, and the known quantities to the other...