 | 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....part, together with the square of the other part. L et the straight line AB be divided into any J^ CB two parts in the point C ; the squares of AB, BC,... | |
 | 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,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. i> K Proved by showing that AB* + uc*... | |
 | Euclides - 1840 - 82 σελίδες
...is equal to the square of the line made up of the half and the produced part. DA PROP. VII. THEOR. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. PROP. VIII. THEOR. If a straight line... | |
 | Euclides - 1840 - 192 σελίδες
...the produced part. PROP. VII. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the squares of the whole line and of one of the parts,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. Upon AB construct the square ACDB ;... | |
 | 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,...whole and that part, together with the square of the otherpart. Let the straight line AB be divided into any two parts in the point C; the squares of AB,... | |
 | 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...part, together with the square of the other part. L et the straight line AB be divided into any j^_ CB two parts in the point C ; the squares of AB,... | |
 | Euclides - 1842 - 316 σελίδες
...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... | |
 | 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,...part, together with the square of the other part. 8. If two circles touch one another internally, they shall not have the same centre. 9. Draw a straight... | |
 | John Playfair - 1844 - 338 σελίδες
...then, AD=2a+6, and CD=a+6. Now by multiplication, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one...part, together with the square of the other part. two parts in the point C ; the squares of AB, BC, are equal to twice the rectangle AB.BC, together... | |
 | Great Britain. Council on Education - 1845 - 696 σελίδες
...described upon the other two sides of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into any two parts,...part, together with the square of the other part. 62. To divide a given straight line into two parts, so that the rectangle contained by the whole, and... | |
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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... 
