 | 1863 - 300 Seiten
...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 - 122 Seiten
...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 - 316 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 - 336 Seiten
...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 Seiten
...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 Seiten
...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 - 434 Seiten
...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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IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 
