An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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... right angles to PAGE 87 18 . To find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola EXAMPLES ཉ་ྲ 91 92 CHAPTER V. TRIANGULAR CO - ORDINATES ...
... right angles to PAGE 87 18 . To find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola EXAMPLES ཉ་ྲ 91 92 CHAPTER V. TRIANGULAR CO - ORDINATES ...
Page 8
... right angles to BC . COR . It may hence be shewn that the three straight lines drawn through the angular points of a ... angle of the triangle of reference . For the internal bisector of the angle A , we shall have , making the same ...
... right angles to BC . COR . It may hence be shewn that the three straight lines drawn through the angular points of a ... angle of the triangle of reference . For the internal bisector of the angle A , we shall have , making the same ...
Page 19
... angle A , then , by the result of the last article , - tan -na ) + ( ma - lb ) 2 tan 0 ( lcna ) — ( ma - lb ) = tan e ... right angles to one another , Hence 1 + tan 0 tan 0 ' = 0 . A ( lc — na ) ( l'c — n'u ) + ( ma — lb ) ( m'a — l'b ) ...
... angle A , then , by the result of the last article , - tan -na ) + ( ma - lb ) 2 tan 0 ( lcna ) — ( ma - lb ) = tan e ... right angles to one another , Hence 1 + tan 0 tan 0 ' = 0 . A ( lc — na ) ( l'c — n'u ) + ( ma — lb ) ( m'a — l'b ) ...
Page 22
... right angles to βγ γ 18 + 2 = 0 , 1 + 1 = 0 , α α = 0 ; α α b and thence prove that they intersect in a point . 3. If be the angle between the two straight lines ( l , m , n ) ( λ , μ , v ) , prove that cot @ = - lλ + mμ + nv − ( mv + ...
... right angles to βγ γ 18 + 2 = 0 , 1 + 1 = 0 , α α = 0 ; α α b and thence prove that they intersect in a point . 3. If be the angle between the two straight lines ( l , m , n ) ( λ , μ , v ) , prove that cot @ = - lλ + mμ + nv − ( mv + ...
Page 51
... angles 2A , 2B , 2C be greater than two right angles , or unless the triangle of reference be obtuse - angled . COR . By referring to the expressions for the co - ordinates of the centre of the conic , given in Art . 17 , we see that at ...
... angles 2A , 2B , 2C be greater than two right angles , or unless the triangle of reference be obtuse - angled . COR . By referring to the expressions for the co - ordinates of the centre of the conic , given in Art . 17 , we see that at ...
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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