| Robert Simson - 1806 - 518 Seiten
...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 : buf the gnomon CMG and LG make up the whole figure CEFD, which is the... | |
| Euclid - 1810 - 518 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...to the square of CD. Wherefore, if a straight line,** 8cc. QED PROP. VII. THEOR. IF a straight line be divided into any two parts, the squares of the whole... | |
| Euclides - 1814 - 558 Seiten
...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...Wherefore, if a straight line, &c. QED PROP. VII.** THEOR. IF a straight line be divided into any two parts, the squares of the whole line, and of one... | |
| Euclides - 1816 - 528 Seiten
....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... | |
| John Mason Good - 1819 - 740 Seiten
...square of the straight line which is made up of the half and. the part produced. Prop. VII. Theor. **If a straight line be divided into any two parts, the squares of the whole line,** ajid of one of the parts, are equal to twice the rectangle contained by the whole and that part, together... | |
| John Playfair - 1819 - 317 Seiten
...Let the straight line AB be bisected in C, and produced to the point A B k) ; the rectangle AD.DB, **together with the square of CB, is equal to the square of CD.** Upon CD describe (46. 1.) the square CEFDJoin DE, and through B draw (31. 1 .) BHG parallel to CE or... | |
| Euclides - 1821 - 294 Seiten
...together with the D 5 of the line drawn to base is = to the square of the side. PROP. 7, THEOR. Mf a right **line be divided into any two parts, the squares of the whole line and** either segment are: equal to double the rectangle under the whole line and that segment, together with... | |
| Rev. John Allen - 1822 - 516 Seiten
...rectangle ZBD being equal to the rectangle ADB, because ZA is equal to BD and ZB to AD, the rectangle ADB **with the square of CB, is equal to the square of CD.** Scholium. — A like observation, as is made in the scholium to prop. 3 of this book, is applicable... | |
| Euclid - 1822 - 179 Seiten
...to the base, equal to the square of the side (2). PROP. VII. THEOR. * Fig. is. If a right line (AB) **be divided into any two parts, the squares of the whole line** ( AB) and either segment (CB) are together equal to double the rectangle under the whole and that segment,... | |
| Peter Nicholson - 1825 - 372 Seiten
...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... | |
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