A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 437
... latus rectum of the parabola GAK , L × AN = NP ' = EN X NF . L = EN X = AL X = NF AF AL AL BL ᏴᏞ ' · PROP . X. If a right cone BAD be cut by a plane AMP through both slant sides , the section is an ellipse . Let BAD be that position ...
... latus rectum of the parabola GAK , L × AN = NP ' = EN X NF . L = EN X = AL X = NF AF AL AL BL ᏴᏞ ' · PROP . X. If a right cone BAD be cut by a plane AMP through both slant sides , the section is an ellipse . Let BAD be that position ...
Page 451
... latus rectum of the parabola . 13. The part of the axis intercepted between its vertex and the point in which it is intersected by one of its own ordinates , is called the abscissa of the axis . 14. The part of the axis intercepted ...
... latus rectum of the parabola . 13. The part of the axis intercepted between its vertex and the point in which it is intersected by one of its own ordinates , is called the abscissa of the axis . 14. The part of the axis intercepted ...
Page 452
... latus rectum is equal to four times the distance from the focus to the vertex . That is , For , LI = 4 AS . N LI = 2 LS , Def . ( 14. ) cor . K = 2 LN A = 2 SK - 4 AS ·· AS = AK . PROP . III . To draw a tangent to the 452 CONIC SECTIONS .
... latus rectum is equal to four times the distance from the focus to the vertex . That is , For , LI = 4 AS . N LI = 2 LS , Def . ( 14. ) cor . K = 2 LN A = 2 SK - 4 AS ·· AS = AK . PROP . III . To draw a tangent to the 452 CONIC SECTIONS .
Page 454
... latus rectum . That is , MG = L if we denote the latus rectum by L. For , MG SG - SM = SP SM . = AS + AM SM . = AS + AS + SM = 2 AS Prop . 3. cor.4 . Prop . 1 . SM --- = L Prop . 2 . M PROP . VI . If a straight line be drawn from the ...
... latus rectum . That is , MG = L if we denote the latus rectum by L. For , MG SG - SM = SP SM . = AS + AM SM . = AS + AS + SM = 2 AS Prop . 3. cor.4 . Prop . 1 . SM --- = L Prop . 2 . M PROP . VI . If a straight line be drawn from the ...
Page 455
... latus rectum and the abscissa . That is , if P be any point in the curve For , PM2 = L. AM . Geom . Theor . 34 . PM2 SP2 - SM2 = ( AM + AS ) - ( AM - AS ) ' = SP AM + AS ( Prop . 1 ) , & SM = AM - AS = 4 AS . AM . Geom . Theor . 31 & 32 ...
... latus rectum and the abscissa . That is , if P be any point in the curve For , PM2 = L. AM . Geom . Theor . 34 . PM2 SP2 - SM2 = ( AM + AS ) - ( AM - AS ) ' = SP AM + AS ( Prop . 1 ) , & SM = AM - AS = 4 AS . AM . Geom . Theor . 31 & 32 ...
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Common terms and phrases
algebraic axis bisected called centre circle circumference coefficient contained Corol cosec cosine cube root curve decimal denominator denote diameter difference differential co-efficient distance Divide dividend division divisor draw dy dx equal EXAMPLES exponent expression extract factors feet figure fraction given number greater greatest common measure Hence hyperbola inches latus rectum least common multiple logarithm manner monomial multiply negative nth root number of terms parallel parallelogram perpendicular plane polynomial positive Prob problem Prop proportional proposed equation quotient radius ratio rectangle Reduce remainder right angles rule sides sine square root straight line Substituting subtract tangent Taylor's theorem THEOREM unknown quantity VULGAR FRACTIONS whole number yards