...explained more fully in another place. GEOMETRY. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute...

...explained more fully in another place. PROPOSITION XII. THEOREM. In every triangle, the square of aside opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute...

...triangles: hence EF(jH is double of ABCD. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute...

...to the rectangle under the other side and its produced part. The square on the side subtending that acute angle is less than the sum of the squares on the sides which contain that angle, by double the rectangle under the side to which the perpendicular is drawn,...

...part. 7. 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 those sides and the straight line intercepted between the perpendicular let fall upon it...

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...have introduced a supposition which changes it into one which is right-angle 1. THEOREM XL I. In any triangle, the square on a side opposite an acute angle is less than the sum of the squares on the other two sides, by twice the rectangle contained by either of these sides, and the distance from the...

...THEOREM. In every triangle, the square on the side subtending either of the acute ungles, 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...

...THEOREM. In every triangle, the square on the side subtending any 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 perpendicular let fall upon it...

...PROPOSITION 13.— THEOREM. In every triangle, the square on the side subtending an acute angle, 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 perpendicular let fall on it from...