PROP. IX. 99 PROP. IX. THEOR. If a st. line be divided into two equal parts, and also into two unequal parts, the squares of the two unequal parts are together double of the square of the half line and of the square of the line between the points of section. CON. 11. 1, 3. I, Pst. 1. 31. I. DEM. 5. 1, 32. I, 29. I, 6. I, 47. I, 34. I, Ax. 1. Scu. 1. The sum of the squares of any two lines is equal to twice the square of half their sum together with nece the square of half their difference. 2. The sum of the squares is equal to half the square of the sum together with half the square of the difference. BOOK II. 101 PROP. X. THEOR. If a st. line be bisected and produced to any point, the square of the whole line thus produced, and the square of the part of it produced are together double of the square of half the line and of the square of the line made up of the half and the part produced. CON. 11. I, 3. I, 31. I, Pst. 1. DEM. 29. I, Ax. 9. 12. 5. I, 32. I, 15. I, 6. I, 34. I, 36. I, 47. I. SCH. 1. The sum of the squares of any two lines is equal to twice the square of half their sum together with t the square of half their difference. 2. The sum of the squares is equal to half the square of the sum together with half the square of the differenc BOOK II. Frop. X. Tapos If a st. line be bisected and produced to any point, the square of the whole line thus produced, and the square of the part of it produced are together double of the square of half the line and of the square of the line made up of the half and the part produced. C. III, 3. 1, 31. I, Pst. J Dax 2), I, Ax. 9. 12. 3. I, 32. I, 15. I, 6. I, 34. I, 36. I, 47. I. 103 |