...Prove that if a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle...the whole and that part, together with the square on the other part. Give Euclid's demonstration of this proposition ; also, prove it algebraically....

...VII. THEOREM. lf a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by tlie whole and that part, toaetlier with the square on the other part. Let the straight line AB be...

...AC is double of the squares of AD and DE. 24. Divide a given straight line into two parts, snch that the squares of the whole line and of one of the parts shall be equal to twice the square of the other part. 25. In any triangle, if a line be drawn from...

...7. THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle...the whole and that part, together with, the square on the other part. Let the straight line AB be divided into any two parts at the point C ': the squares...

...Parallelograms upon equal bases and between the same parallels are equal. 4. Prove Prop. 47, BI 5. If a straight line be divided into any two parts, the...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. 6. If a straight line touch a circle,...

...child go ? 11. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle...the whole and that part, together with the square on the other part. Where does Euclid afterwards use this proposition? 12. To inscribe a square in a...

...line be divided into an; two parts, the squares of the whole line and one of the parti are together equal to twice the rectangle contained by the whole...part, together with the square of the other part. 3. In an obtuse angled triangle, if a perpendicular be drawn from either of the acute angles to the...

...line be divided into any two parts : then the squares of the whole line and one of the parts shall be equal to twice the rectangle contained by the whole...that part together with the square of the other part. 4. The square of the difference of two numbers is equal to the sum of the squares of the two numbers...

...If a straight line be divided into any two parts, the squares on the whole line, and on one of Uie parts, are equal to twice the rectangle contained...the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C. Then the...

...= li8— = 7952.4 miles; and 7952.4-2.5= 7949.9, the earth's diameter. PBOP. 7. — THEOB. If a st. line be divided into any two parts, the squares of...contained by the whole and that part, together with a square of the other part. Cons.— 46. I., Pst. 1 and 31. I. DEM. — 43. I., AM. 2 and 6, Def. 30....