An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page x
... right angles to one another . Directrix of a Parabola 21 . To find the magnitudes of the axes of the Conic 355 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola EXAMPLES . 388 96 ...
... right angles to one another . Directrix of a Parabola 21 . To find the magnitudes of the axes of the Conic 355 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola EXAMPLES . 388 96 ...
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
... right angles to one another . If 0 , ' be the respective inclinations of these straight lines to the internal bisector of the angle A , then , by the result of the last article , ( lcna ) - ( ma - lb ) A tan e = tan ( lcna ) + ( ma — lb ) ...
... right angles to one another . If 0 , ' be the respective inclinations of these straight lines to the internal bisector of the angle A , then , by the result of the last article , ( lcna ) - ( ma - lb ) A tan e = tan ( lcna ) + ( ma — lb ) ...
Page 22
... right angles to α 8 + 20 , +0 + 8 = 0 ; - = а γ = b c b a 0 , - a 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 0 = - DA + mutnv ...
... right angles to α 8 + 20 , +0 + 8 = 0 ; - = а γ = b c b a 0 , - a 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 0 = - DA + mutnv ...
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 . 18 , 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 . 18 , we see that at ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²