| 1863
...9. Divide an equilateral trianglo into four equal triangles. Book 2. 10. Proposition 7, Theorem ; It **a straight line be divided into any two parts the squares of the whole line, and** one of the parts, are equal to twice the rectangle contained by the whole and that part, together with... | |
| Euclides - 1863
...the rectangle AD. DB. To each of these equals add LG, which is equal to the square of CB. Therefore **the rectangle AD. DB, together with the square of CB, is equal to the** gnomon CMG, and LG. But tho gnomon CMG and LG make up thesquare CF, which is the square of CD. Therefore... | |
| University of Oxford - 1863
...with the square on the line between the points of section, is equal to the square on half the line. 9. **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 contained by the whole and... | |
| Euclides - 1864 - 262 páginas
...the square on CB, is equal to the square on CD. Wherefore, if a straight line, &c. QED PROPOSITION **VII. THEOREM. If a straight line be divided into any two parts, the squares** on the whole tine, and on one of the parts, are equal to twice the rectangle contained by the whole... | |
| Euclides - 1864 - 448 páginas
...BD, and by A, DE, and by A, EC. Wherefore, if there be two straight lines, &c. QED PROPOSITION II. **THEOREM. If a straight line be divided into any two parts, the** rectangles contain! 'I by the whole and each of the parts, are together equal to the square on I he... | |
| Euclides - 1865 - 402 páginas
...LG; but the gnomon CMG and LG make up the whole figure CEFD, which is the square of CD ; therefore **the rectangle AD, DB, together with the square of...the square of CD. Wherefore, if a straight line, &c.** QE Du PROP. VII.— THEOREM. If a straight line be divided into any two parts ; then the squares of... | |
| Queensland. Department of Public Instruction - 1866
...proposition in the case of a triangle whose sides are 3, 4, and 5 units respectively. 5. 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 contained by the whole... | |
| Euclid, Isaac Todhunter - 1867 - 426 páginas
...the square on CB, is equal to the square on CD. Wherefore, if a straight line &c. QED PUO POSITION 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 contained by the whole... | |
| Euclid, Isaac Todhunter - 1867 - 424 páginas
...the square on CB, is equal to the square on CD. Wherefore, if a straight line &c. QED PROPOSITION 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 contained by the whole... | |
| Robert Potts - 1868 - 410 páginas
...of which DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. **THEOREM. If a straight line be divided into any two parts, the** rectangle contained ky the whole and one of the parts, is equal to the rectangle contained by the twa... | |
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