The Principles of Analytical Geometry ...

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J. Deighton & sons, 1826 - 326 من الصفحات
 

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

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