A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 188
... prop . VIII . = and hence subtracting these b equal quantities from unity , a Or , a C a с d = a C Or , a с - i . e ... Prop . IX . a + b = c + d d And , a + b By Prop . X. b 138 ALGEBRA .
... prop . VIII . = and hence subtracting these b equal quantities from unity , a Or , a C a с d = a C Or , a с - i . e ... Prop . IX . a + b = c + d d And , a + b By Prop . X. b 138 ALGEBRA .
Page 189
... Prop . X. b Dividing these equals by each other , a + b b a b = c + d C d d = c + d Or , a + c + d = a C d i . e . a + bab :: c + d : c - d XIII . If there be any number of quantities more than two , and as many others . which , taken ...
... Prop . X. b Dividing these equals by each other , a + b b a b = c + d C d d = c + d Or , a + c + d = a C d i . e . a + bab :: c + d : c - d XIII . If there be any number of quantities more than two , and as many others . which , taken ...
Page 380
... PROP . I. The distance of the focus from any point in the curve , is equal to the sum of the abscissa of the axis corresponding to that point , and the distance from the focus to the vertex . That is , ! For , SP = AM + AS . N SP PN ...
... PROP . I. The distance of the focus from any point in the curve , is equal to the sum of the abscissa of the axis corresponding to that point , and the distance from the focus to the vertex . That is , ! For , SP = AM + AS . N SP PN ...
Page 382
... Prop . 3. cor . 2 . = MS + SA + AM . Prop . 1 . T A S M = 2 AM . Cor . MT is bisected in A. PROP . V. The subnormal is equal to one half of the latus rectum . That is , MG = L if we denote the latus rectum by L. For , MG SG- SM = SP SM ...
... Prop . 3. cor . 2 . = MS + SA + AM . Prop . 1 . T A S M = 2 AM . Cor . MT is bisected in A. PROP . V. The subnormal is equal to one half of the latus rectum . That is , MG = L if we denote the latus rectum by L. For , MG SG- SM = SP SM ...
Page 383
... Prop . 4. , TA = AM .. Since AY cuts the sides of A TPM pro- portionally , AY is parallel to MP , . : . AY is ... Prop . 3. cor . 2 . SY2 SP = SA And since SA is constant for the same parabola , SP ∞ SY2 . Cor . 4. By Cor . 1. , SY 2 ...
... Prop . 4. , TA = AM .. Since AY cuts the sides of A TPM pro- portionally , AY is parallel to MP , . : . AY is ... Prop . 3. cor . 2 . SY2 SP = SA And since SA is constant for the same parabola , SP ∞ SY2 . Cor . 4. By Cor . 1. , SY 2 ...
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algebraic ALGEBRAIC QUANTITIES altitude axis base bisected body centre chord circle circumference co-ordinates Corol cosec cosine cube curve decimal denominator diameter difference differential co-efficient distance divide divisor draw dy dx equal equation Example exponent expression extract feet figure force fraction given gravity Hence hyperbola inches latus rectum least common multiple length logarithm manner monomial multiply nth root number of terms parabola parallel parallelogram perpendicular polynomial Prob PROBLEM PROP proportional quotient radius ratio rectangle reduced right angles rule sides sine specific gravity square root straight line Substituting subtract tangent THEOREM triangle ABC unknown quantity velocity VULGAR FRACTIONS weight whole number yards