 | John Playfair - 1806 - 320 σελίδες
...AB2=AC2+CBJ+2AC.CB. Wherefore, if a straight line be divided, &c. QED COR. From the demonstration it is manifest that the parallelograms about the diameter of a square are likewise squares. . PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts,... | |
 | Euclid - 1810 - 554 σελίδες
...rectangle AC, CB. Wherefore, if a straight line, &c. QED CoR. From the demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, aid also into two unequal parts... | |
 | John Playfair - 1819 - 350 σελίδες
...+2AC.CB. Wherefore, if a straight line be divided &c. QED COR. From the demonstration, it is manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight line be divided into two equal parts, and also into two uneqtial parts... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...rectangle AC, CB. Wherefore, if a straight line, &c. Gt. ED Cor. From the demonstration, it is manifest, that the parallelograms about the diameter of a square, are likewise squares. Proposition V. Tlieorem. If a straight line be divided into two equal parts, and also into two unequal... | |
 | George Lees - 1826 - 276 σελίδες
...AC2+CB2+2AC.CB. Wherefore, if a straight line, &c. QED Cor. 1. From this demonstration, it is manifest that the parallelograms about the diameter of a square are likewise squares. Cor. 9,. The square of any line is equivalent to four times the square of half the line. Cor. 3. If... | |
 | Euclid - 1835 - 540 σελίδες
...rectangle AC, CB. Wherefore, " if a straight line," &c. QED COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square are likewise squares. e6. I. f34. I. 8 ^ '• a 46. 1. b31. 1. c 43. 1. PROP. V. THEOR. If a straight line be divided into... | |
 | 1836 - 488 σελίδες
...together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the parallelograms about the diameter of a square are likewise squares. V. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle... | |
 | Robert Simson - 1838 - 434 σελίδες
...rectangle AC, CB. Wherefore, if a straight line, &c. QED COR. From the demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts... | |
 | Euclides - 1842 - 316 σελίδες
...rectangle AC, CB. Wherefore, if a straight line, &c. QED COR. From the demonstration it is manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts,... | |
 | John Playfair - 1842 - 332 σελίδες
...GE=the figure AE, or AB2; therefore AB2= AC2+CB2+2AC.CB. COR. From the demonstration, it is manifest that the parallelograms about the diameter of a square are likewise squares. SCHOLIUM. This property is derived from the square of a binomial. For, let the two parts into which... | |
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IF a straight line be divided into two equal parts, and also into two unequal parts : the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 
