An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
From inside the book
Results 1-5 of 18
Page 1
... sides respectively opposite to them by a , b , c , and the dis- tances of any point from BC , CA , AB respectively by the letters a , ẞ , y . When two points lie on opposite sides of a line of re- ference , the distance of one of these ...
... sides respectively opposite to them by a , b , c , and the dis- tances of any point from BC , CA , AB respectively by the letters a , ẞ , y . When two points lie on opposite sides of a line of re- ference , the distance of one of these ...
Page 7
... opposite sides , intersect in a point . For these straight lines will be represented by the equations bB = cv , cy = aa , aa = Bb , and , therefore , all pass through the point for which aa = bB = cy . In the next three propositions the ...
... opposite sides , intersect in a point . For these straight lines will be represented by the equations bB = cv , cy = aa , aa = Bb , and , therefore , all pass through the point for which aa = bB = cy . In the next three propositions the ...
Page 8
... opposite side . Making a construction similar to that in the last proposi- tion , it will be seen that we have here ... sides , intersect in the point determined by the equations a cos A = ẞ cos B : = Y cos C. 6. To find the equations of ...
... opposite side . Making a construction similar to that in the last proposi- tion , it will be seen that we have here ... sides , intersect in the point determined by the equations a cos A = ẞ cos B : = Y cos C. 6. To find the equations of ...
Page 9
... sides opposite to them , lie in the same straight line ; and also that the points in which the external bisector of any one angle , and the internal bisectors of the other two angles , intersect the sides respectively opposite to them ...
... sides opposite to them , lie in the same straight line ; and also that the points in which the external bisector of any one angle , and the internal bisectors of the other two angles , intersect the sides respectively opposite to them ...
Page 30
... sides opposite to them , lie in the same straight line ; and that the points in which the external bisector of any one angle and the internal bisectors of the other two angles , intersect the sides respectively opposite to them , lie in ...
... sides opposite to them , lie in the same straight line ; and that the points in which the external bisector of any one angle and the internal bisectors of the other two angles , intersect the sides respectively opposite to them , lie in ...
Other editions - View all
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