 | Euclides - 1838 - 264 pages
...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 CB, is equal to the square of CD. Wherefore, if a straight line, Ac. «,in D. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...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... | |
 | Euclides - Geometry - 1841 - 378 pages
...the rectangle AD, DB: add to each of these equals 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... | |
 | Euclides - 1842 - 316 pages
...is equivalent to the square of C D. Wherefore, if a straight line, &c. QED РRОР. VII. ТНЕОВ, IF a straight line be divided into any two parts : the squares of the whole line, and one of the parts, are equivalent to twice the rectangle contained by the whole and that part, together... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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 - Geometry - 1845 - 218 pages
...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... | |
 | Euclides - 1845 - 546 pages
...the rectangle AD, DB : add to each of these equals 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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...and CA ; therefore NB is equal (I. ax. 2) to AD. NA cap 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. PROP. VII. THEOB. — If a straight line be divided into any two parts, the... | |
 | Euclides - 1846 - 292 pages
...is equal to the gnomon CMG : To each of these 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 the figure LG : But the gnomon CMG and LG make up the whole figure CEFD, which is the... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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... | |
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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. 
