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according angle applied assumed asymptotes axes axis base becomes called centre CHAP chords circle co-ordinates coincides conjugate diameters constructed contained corresponding curve denote described determined difference direction distance dividing draw drawn dropped ellipse ellipse and hyperbola equal equation equation becomes evident expressed find the equation follows former formulas geometrical given point Hence hyperbola imaginary inclination infinite join known latter locus magnitude manner means meet negative obtained origin parabola parallel passes perpendicular plane positive PROB problem produced projection PROP proposition proved quantity radius rectangular referred represent respectively right angles roots second order sides similar situated solution sought square straight line substitution supposed surface system of conjugate tangent trace triangle values whence
Page 7 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 1 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 244 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 116 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the...
Page 66 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Page 115 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 14 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 68 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Page 79 - If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments.