...the parallelogram AHKB will be double of either of the triangles EDG or ECF. 3. If a straight line be divided into two equal parts and also into two unequal...contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 4. Divide a given...

...third side, then the two sides contain a right angle. 6. If a straight line is divided into two equal, and also into two unequal parts, the rectangle contained by the unequal parts, etc. Complete this examination and prove the theorem. 7. ABCD is a square, each side of which is eight...

...produced, the exterior angle is greater than either of the interior remote angles. 4. If a straight line be divided into two equal parts, and also into two unequal...section, is equal to the square of half the line. 5. If a straight line be divided into any two parts, the squares of the whole line and of one of the...

...drawing parallels to the sides, shall be a rhombus. 4. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained...between the points of section is equal to the square on half the line. 5. Shew how to divide a given straight line internally or externally so that the...

...times their rectangle. Rectangles of equal parts and of unequal parts. 49. THEOREM 15. If a line is divided into two equal parts, and also into two unequal parts, the rectangle of the unequal parts, together with the square on the intermediate part, is equivalent to the square...

...unequal parts; show that the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. A straight line is divided into two parts; show that the rectangle contained by the...

...equally and also unequally, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. I. 46. I. 31. I. 43. Let the straight line AB be divided equally at P, and unequally...

...theorem you have that the rectangle upon the two unequal segments, which is 21 by construction, plus the square of the line between the points of section, is equal to 25, the square on half the line. This gives 25 — 21 or 4, as the square of that length, 2 as the...

...the interior angles upon the same side together equal to two right angles. 3. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal (Kirts together with the square of the line between the poiuts of section, is equal to the square of...

...parallelogram are equal to one another, and the diagonal bisects the area ? 4. If a straight line be divided into two equal parts, and also into two unequal parts, the squares of the unequal parts are together double of the square of half the line, and of the square...