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Side 11 - 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.
Side 3 - 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.
Side 248 - 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.
Side 120 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the...
Side 70 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Side 119 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Side 18 - 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...
Side 72 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Side 83 - 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.
Side 257 - It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle.