An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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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
... straight line to AB , AC , are determined . 17. To find the condition that two ... angle A , then , by the result of the last article , ( lcna ) + ( ma — lb ) ... right angles to one another , Hence 1 + tan 0 tan 0 ′ = 0 . ( lc - na ) ( l ...
... straight line to AB , AC , are determined . 17. To find the condition that two ... angle A , then , by the result of the last article , ( lcna ) + ( ma — lb ) ... right angles to one another , Hence 1 + tan 0 tan 0 ′ = 0 . ( lc - na ) ( l ...
Page 22
... straight lines , drawn through the several angular points of the triangle of reference , respectively at right angles to β γ + = 0 , + b с γ α b α α B = 0 , + a b = 0 ; and thence prove that they intersect in a point . 3. If be the angle ...
... straight lines , drawn through the several angular points of the triangle of reference , respectively at right angles to β γ + = 0 , + b с γ α b α α B = 0 , + a b = 0 ; and thence prove that they intersect in a point . 3. If be the angle ...
Page 119
... right angle at S , or by bb ' being a right angle . Again , the fact that OC is perpendicular to AB , shews that cSc ' is a right angle . Then the reciprocal theorem tells us that a Sa ' is also a right angle . We may express this more ...
... right angle at S , or by bb ' being a right angle . Again , the fact that OC is perpendicular to AB , shews that cSc ' is a right angle . Then the reciprocal theorem tells us that a Sa ' is also a right angle . We may express this more ...
Page 120
... right angles to OA ' , OB , OC ' , then YZ , ZX , XY are respectively parallel to BC , CA , AB , or the triangle XYZ is similar and similarly situated to the triangle ABC . We may observe further , that the point X , since it is the ...
... right angles to OA ' , OB , OC ' , then YZ , ZX , XY are respectively parallel to BC , CA , AB , or the triangle XYZ is similar and similarly situated to the triangle ABC . We may observe further , that the point X , since it is the ...
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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