Uniplanar Algebra: Being Part I of a Propædeutic to the Higher Mathematical AnalysisBerkeley Press, 1893 - 141페이지 |
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addition and subtraction Addition Theorem affix Agenda amplitude angle AOQ arc-ratio assumed base called circular sector cis ß co-ordinates commutative laws complex quantities corresponding cosh COSK csch defined definition direction distance equal equation equilateral hyperbola expm exponential expressed factors formula functions geometric addition geometric multiplication Goniometric Ratios Hence hyperbolic functions Hyperbolic Ratios hyperbolic sector imaginary indeterminate form integer inverse law of geometric law of indices law of involution law of metathesis length logarithmic spiral logarithms logm modular normal modulus natural logarithms negative nth root parallel path perpendicular plane polynomial positive Prop PROPOSITION Prove the following quotient radius rational numbers real axis real magnitudes real quantities respectively sech sinh straight line tanh tensor tion triangle u+iv unit circle z-plane zero
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9 페이지 - Magnitudes which have the same ratio to the same magnitude, are equal to one another: and those to which the same magnitude has the same ratio, are, equal to one another.
8 페이지 - Equal magnitudes have the same ratio to the same magnitude : and the same has the same ratio to equal magnitudes.
7 페이지 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
36 페이지 - In any proportion, the product of the means is equal to the product of the extremes.
10 페이지 - That magnitude which has a greater ratio than another has unto the same magnitude, is the greater of the two : and that magnitude to which the same has a greater ratio than it has unto another . magnitude, is the less of the two.
9 페이지 - Of unequal magnitudes the greater has a greater ratio to the same than the less has : and the same magnitude has a greater ratio to the less than it has to the greater.
3 페이지 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, when the less is contained a certain number of times exactly in the greater.
4 페이지 - The ratio of one magnitude to another of the same kind is the quotient obtained by dividing the numerical measure of the first by that of the second, the unit being the same in each case.
7 페이지 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
5 페이지 - B, according as mP is greater than, equal to, or less than »Q, whatever whole numbers m and n may be. It is an immediate consequence that: The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and...