An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 1-5 of 20
Page 8
... tion , it will be seen that we have here DE . AC DF . AB cos B Cos C ; each of these fractions being equal to the area of the triangle ABC . or Hence PG.AC cos B PH.AB cos C ; B cos B = Y cos C. This will be the equation of the straight ...
... tion , it will be seen that we have here DE . AC DF . AB cos B Cos C ; each of these fractions being equal to the area of the triangle ABC . or Hence PG.AC cos B PH.AB cos C ; B cos B = Y cos C. This will be the equation of the straight ...
Page 16
... tion ( 4 ) may be looked upon as an expression of the fact that two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , ß , y , or , in other words , that the two straight lines ...
... tion ( 4 ) may be looked upon as an expression of the fact that two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , ß , 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 aa + 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 aa + bB + cy = 0 is , in itself , impossible , -in fact , a ...
Page 32
... two points . It is not difficult to see that , if a system of straight lines in involution be cut by a transversal , the points of sec- tion will also be in involution . 33 CHAPTER II . SPECIAL FORMS OF THE EQUATION OF 32 MODERN GEOMETRY .
... two points . It is not difficult to see that , if a system of straight lines in involution be cut by a transversal , the points of sec- tion will also be in involution . 33 CHAPTER II . SPECIAL FORMS OF THE EQUATION OF 32 MODERN GEOMETRY .
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 , coinci- dent ...
... 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 , coinci- dent ...
Other editions - View all
Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα