 | 1836 - 488 σελίδες
...is equal to the square of the straight line which is made up of the half and the part produced. VII. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Сон. Hence the sum of the squares of... | |
 | Euclides - 1837 - 112 σελίδες
...these = AL + CM + LG, which = AM + LG, and that these last = AD X DB + CB*. PROPOSITION VII. Theorem. If a straight line be divided into any two parts,...part, together with the square of the other part. i> K Proved by showing that AB* + uc* = figs. AG + GE + 2 CH + KF, and that these = 2 AH + KF ; ;and... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...figure, as there will remain the rectangle AM and the square LG, together equal to tb« square CF. IF a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into... | |
 | John Playfair - 1837 - 332 σελίδες
...to each member of the equality, we shall have, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one....equal to twice the rectangle contained by the whole and that part, together with the square of the other part. L et the straight line AB be divided into... | |
 | Euclides - 1838 - 264 σελίδες
...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...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into... | |
 | Euclid - 1838 - 470 σελίδες
...of CB, is equal to 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...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into... | |
 | Euclides - 1840 - 192 σελίδες
...square of the sum of the whole line AB and one of its parts CB, is equal to 4 AB'CB, or four times the rectangle contained by the whole line and that part, together with AC2 or the square of the other part. PROP. IX. THEOR. If a straight line (AB) be divided equally (in... | |
 | Euclides - 1841 - 378 σελίδες
...equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. VII. THEOR. *36. 1. a * 43. 1. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the otherpart. Let the straight line AB be divided into... | |
 | John Playfair - 1842 - 332 σελίδες
...to each member of the equality, we shall have, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. L et the straight line AB be divided into... | |
 | 1844 - 688 σελίδες
...equal to the rectangles contained by the undivided line and the several parts of the divided line. 7. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 8. If two circles touch one another internally,... | |
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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. Let the straight line AB be divided... 
