## Uniplanar Algebra: Being Part I of a Prop©¡deutic to the Higher Mathematical Analysis |

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according addition and subtraction Addition Theorem Agenda algebraic operation amplitude antecedent arc-ratio arcs arithmetic base Benjamin Peirce called chords circular sector coincidence commutative law complex quantities consequent construction Corollary corresponding cosh cosK defined definition denoted distance equation equimultiples expK exponential formula geometric addition given ratio Goniometric Ratios Hence hyperbolic functions Hyperbolic Ratios hyperbolic sector imaginary indeterminate form integers intercept intersect inverse law of indices law of involution law of metathesis length less logarithmic spirals logarithms logK modulus Multiplication and Division natural logarithms negative factors negative magnitude nth roots Orthomorphosis plane Plane Geometry polynomial proof Prop proportion Proposition Proposition 13 prove quotient radii radius ratio are equal real axis real magnitudes real quantities real unit reciprocal rectangles represent respectively roots sinh tangent tanh tensor three magnitudes tion triangle unit circle zero

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9 ÆäÀÌÁö - 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 ÆäÀÌÁö - Equal magnitudes have the same ratio to the same magnitude : and the same has the same ratio to equal magnitudes.

7 ÆäÀÌÁö - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.

36 ÆäÀÌÁö - In any proportion, the product of the means is equal to the product of the extremes.

10 ÆäÀÌÁö - 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 ÆäÀÌÁö - 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 ÆäÀÌÁö - 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 ÆäÀÌÁö - 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 ÆäÀÌÁö - 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 ÆäÀÌÁö - 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...