An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... tion · • · 2 , 3. Equation of the Conic described about the Triangle of Refer- 33333 ence 34 · · • 4 . Position of the Centre . Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity 37 6 ...
... tion · • · 2 , 3. Equation of the Conic described about the Triangle of Refer- 33333 ence 34 · · • 4 . Position of the Centre . Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity 37 6 ...
Page 8
... tion , it will be seen that we have here = sin DAE = cos C , = DE AD DF = AD sin DAF = cos B ; DE cos C = DF COS B ' Hence PG Cos C PH = or cos B .. PG cos BPH cos C , B cos By cos .C . This will be the equation of the straight line ...
... tion , it will be seen that we have here = sin DAE = cos C , = DE AD DF = AD sin DAF = cos B ; DE cos C = DF COS B ' Hence PG Cos C PH = or cos B .. PG cos BPH cos C , B cos By cos .C . This will be the equation of the straight line ...
Page 16
... tion ( 4 ) may be looked upon as an expression of the fact that the two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , B , y , or , in other words , that the two straight lines ...
... tion ( 4 ) may be looked upon as an expression of the fact that the two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , B , y , or , in other words , that the two straight lines ...
Page 17
... tion , if the conventions on which it is adopted be clearly un- derstood . It is , however , desirable that attention should be called to the fact , that the equation ax + bB + cy = 0 is , in itself , impossible , -in fact , a ...
... tion , if the conventions on which it is adopted be clearly un- derstood . It is , however , desirable that attention should be called to the fact , that the equation ax + bB + cy = 0 is , in itself , impossible , -in fact , a ...
Page 33
... tion , shall investigate the nature of the curve corresponding to certain special forms of the equation . PROP . Every curve represented by an equation of the second degree is cut by a straight line in two points , real , coincident ...
... tion , shall investigate the nature of the curve corresponding to certain special forms of the equation . PROP . Every curve represented by an equation of the second degree is cut by a straight line in two points , real , coincident ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα