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 22
Page 6
... expression for r . It may also be proved in a similar manner that 2.2 = abc 4A2 { a cos △ ( α , — α ) 2 + b cos B ( ß ̧ — ß2 ) 2 - + c cos C ( Y1 — Y1⁄2 ) 3 } • 4. We next proceed to investigate the equation of a straight line ; and ...
... expression for r . It may also be proved in a similar manner that 2.2 = abc 4A2 { a cos △ ( α , — α ) 2 + b cos B ( ß ̧ — ß2 ) 2 - + c cos C ( Y1 — Y1⁄2 ) 3 } • 4. We next proceed to investigate the equation of a straight line ; and ...
Page 16
... 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 represented by them do not intersect ...
... 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 represented by them do not intersect ...
Page 17
... expressed by saying that the equation aa + bB + cy = 0 , or the equivalent equation a sin A + B sin B + y sin C = 0 , represents the straight line at infinity . This phraseology is very convenient , and free from objec- tion , if the ...
... expressed by saying that the equation aa + bB + cy = 0 , or the equivalent equation a sin A + B sin B + y sin C = 0 , represents the straight line at infinity . This phraseology is very convenient , and free from objec- tion , if the ...
Page 21
... expression . It will be observed , that the numerator of this expression vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , as manifestly ought to be the case . : mn It will also be remarked , that the more nearly the ...
... expression . It will be observed , that the numerator of this expression vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , as manifestly ought to be the case . : mn It will also be remarked , that the more nearly the ...
Page 23
... expressed by the notation { 0. PQRS } * . DEF . 2. If P , Q , R , S be four points in a straight line , PQ.RS is called the anharmonic ratio of the range the ratio PS . QR P , Q , R , S , and may be expressed thus [ PQRS ] . In using ...
... expressed by the notation { 0. PQRS } * . DEF . 2. If P , Q , R , S be four points in a straight line , PQ.RS is called the anharmonic ratio of the range the ratio PS . QR P , Q , R , S , and may be expressed thus [ PQRS ] . In using ...
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