...part. Let AB be a given right line. It is required to cut it so that the rectangle contained under the whole line and one part may b~e equal to the square made of the other part. •46.1. Let the square ABC D be describedа on j AB, bisect AC in E, and draw...

...XI. PROBLEM. To cut a given right line into two parts so that the rectangle which is contained under the whole line and one part may be equal to the square made of the other part. * 46. l. Let the square ABCD be described * on Let AB be a given right line....

...one another. 7. Divide a straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part. 8. The three interior angles of every triangle are together equal to two right angles. Prove this,...

...Divide Algebraically a given line a into two parts, such that the rectangle contained by the whole and one part may be equal to the square on the other part. Deduce Euclid's construction from one solution, and explain the other. 37. Given the less segment of...

...'••/£: , 10. Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part, jj yi . 1 1. Give construction only for describing a square equal to a given rectilineal fiigure. JJ-...

...b'y + c'*y = o. 8. Solve ax+ b Vi - x2 = e. 9. Cut a line 1 8 feet long so that the rectangle under the whole line and one part may be equal to the square of the other. 10. A sum of money is divided equally amongst a certain number of persons ; had there...

...hour. (24) Divide a line 20 inches long into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part. (25) Land was bought for 1000 guineas ; and the buyer, after reserving i è acres for himself, sold...

...inch. 14. Divide a line- 20 inches long into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. 15. A can do some work in 9 hours less time than B can do it, and together they can do it in 20 hours....

...other. 5. Divide a given straight line into two parts such that the rectangle contained by the whole and one part may be equal to the square on the other part. 6. In an isosceles triangle ABC, prove that the straight line AD, which bisects the vertical angle...

...points of section; or (я + Ь) (a — b) = a* — b1. II. 9 and 10. — The squares on the same nneqnal segments are together double the squares on the other...square on the base of a triangle is equal to the sum of the squares on the two sides plus or minus (as the vertical angle is obtuse or acule), twice the rectangle...