| Robert Simson - 1827 - 513 sider
...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.** Q. £. JO. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole... | |
| John Playfair - 1829 - 186 sider
...into the parts a and b, and x be equal to s, then sx = ax + bx becomes ss = <zs + bs. PROPOSITION III. **THEOREM. If a straight line be divided into any two parts, the** rectangle contained by the whole line and one of the parts is equal to the square of that part together... | |
| Euclides - 1834
...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...square of CD. Wherefore, if a straight line, &c. QED** PROPOSITION VII. THEOR. — If a straight line be divided into any two parts, the squares of the whole... | |
| Euclid - 1835 - 513 sider
...Cor. 4. 2. rectangle AD, DB : Add to each of these 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 the figure LG : But the gnomon CMG and LG make up the whole figure CEFD, which is the... | |
| John Playfair - 1836 - 114 sider
...equal to the rectangle AD, DB ; add to each of these 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 the figure LG: but the gnomon CMG and LG make up the whole figure CEFD, which is the... | |
| Andrew Bell - 1837 - 240 sider
...to the rectangle AD • DB ; add to each of these 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, together with LG. But the gnomon CMG, together with LG, makes up the whole figure CEFD,... | |
| John Playfair - 1837 - 318 sider
...produced. Let the straight line AB be bisected in C, and produced to the point D ; the rectangle AD.DB **together with the square of CB, is equal to the square of CD.** Upon CD describe (Prop. 46.1.) the square CEFD, join DE, and through B draw (Prop. 31. 1.) BHG parallel... | |
| Euclid, James Thomson - 1837 - 390 sider
...equals CB and CA ; therefore NB is equal (I. ax. 2.) to AD. But (II. 5.) the rectangle NB.BD, or AD.BD, **together with the square of CB, is equal to the square of CD** : which was to be proved. * After it has been proved, as above, that HF is equal to AL, the rest of... | |
| Euclides - 1837 - 88 sider
...Proved by showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV. **Theorem. If a straight line be divided into any two parts, the** square of the whole line is equal to the squares of the two parts together with twice the rectangle... | |
| Euclid - 1838 - 416 sider
...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.** a. ED PROP. VII. THEOR. Ir a straight line be divided into any two parts, the squares of the whole... | |
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