 | Robert Simson - 1806 - 546 σελίδες
...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 - 554 σελίδες
...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 - 560 σελίδες
...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 - 588 σελίδες
....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 - 800 σελίδες
...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 - 354 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 222 σελίδες
...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 - 1046 σελίδες
...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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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. 
