Uniplanar Algebra: Being Part I of a Propædeutic to the Higher Mathematical Analysis |
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Common terms and phrases
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
Popular passages
Page 9 - 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.
Page 8 - Equal magnitudes have the same ratio to the same magnitude : and the same has the same ratio to equal magnitudes.
Page 7 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 36 - In any proportion, the product of the means is equal to the product of the extremes.
Page 10 - 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.
Page 9 - 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.
Page 3 - 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.
Page 4 - 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.
Page 7 - 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.
Page 5 - 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...