 | Euclides - 1837 - 112 sider
...4. that similarly* no other line but BD is in the same right line with BC. PROPOSITION XV. Theorem. If two straight lines cut one another, the vertical, or opposite, angles shall be equal. Steps of the Demonstration. 1. Prove that Zs AEC + AED = 2 right Zs, 2. that Zs AED + DEB = Zs AEC... | |
 | Euclid - 1838 - 470 sider
...greater, which is impossible ; therefore BE is not in the same straight line with BC. And, in like manner, it may be demonstrated that no other can be in the...Wherefore, if at a point, &c. QED PROP. XV. THEOR. Ir two straight lines cut one another, the vertical or opposite angles shall be equal. THE ELEMENTS... | |
 | Euclides - 1842 - 316 sider
...which is impossible ; therefore в Е is not in the same straight line with BC. And, in like manner, it may be demonstrated, that no other can be in the...angles shall be equal. Let the two straight lines AB, c D cut one another in the point E ; the angle AEC shall be equal to the angle DEB, and CEB to AED.... | |
 | John Playfair - 1842 - 332 sider
...greater, which is impossible ; therefore BE is not in the same straight line with BC. And in like manner, it may be demonstrated, that no other can be in the...which therefore is in the same straight line with CB. 1* PROP. XV. THEOR. If two straight lines cut one another, the vertical, or opposite angles are equal.... | |
 | Euclides - 1845 - 546 sider
...which is impossible : therefore BE is not in the same straight line with CB. And in the same manner it may be demonstrated, that no other can be in the...straight line with CB. Wherefore, if at a point, &c. QED PROPOSITION XV. THEOREM. If two straight lines cut one another, the vertical, or opposite angles shall... | |
 | Euclid - 1845 - 218 sider
...greater, which is impossible ; therefore BE is not in the same straight line with BC. And, in like manner, it may be demonstrated, that no other can be in the...straight line with CB. Wherefore, if at a point, &c. QED PROPOSITION XV. THEOR. — If two straight lines cut one another, the vertical or opposite, angles... | |
 | Euclid, James Thomson - 1845 - 382 sider
...not in the same straight line with BC : and in like manner it may be demonstrated, that no other line can be in the same straight' line with it but BD,...straight line with CB. Wherefore, if at a point, &c. Cor. If, at a point in a straight line, two other straight lines meet on the opposite sides of it,... | |
 | Euclid, John Playfair - 1846 - 334 sider
...greater, which is impossible ; therefore BE is not in the same straight line with BC. And in like manner, it may be demonstrated, that no other can be in the...which therefore is in the same straight line with CB. PROP. XV. THEOR. If two straight lines cut one another, the vertical, or opposite angles are equal.... | |
 | Euclides - 1846 - 292 sider
...greater — which is absurd : Therefore BE is not in the same straight line with BC : And in like manner it may be demonstrated, that no other can be in the same straight line with it but BD : Therefore BD is in the same straight line with BC. Wherefore, If at a point S$c. QED PROP. XV. THEOB.... | |
 | Great Britain. Admiralty - 1846 - 128 sider
...BD can be in the same str. line with BC. Wherefore, if at a point, &c. PROP. XIV. THEOR. 15. 1 Eu. If two straight lines cut one another, the vertical or opposite angles shall be equal. Let the str. lines AB, CD, cut one another in E; then /. AEC = L DEB, and /. CEB = L AED. •/str.lineAEmakeswith... | |
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ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. 
