 | 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. is. 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 = /_ DEB, and L CEB = L AED. Vstr.lineAEmakeswithCDthe... | |
 | London univ - 1846 - 326 sider
...proposition, and joining the point of intersection with the vertex of the angle to be bisected. 3. Prove that if two straight lines cut one another, the vertical or opposite angles will be equal. 4. Construct a triangle of which the sides shall be equal to three given straight lines.... | |
 | Euclides - 1847 - 128 sider
...the same pt. The said lines, however, are not in the same st. line. PROP. XV. THEOR. GEN. ENUN. — If two straight lines cut one another, the vertical, or opposite, angles shall be equal. PART. ENUN. — Let the two st. lines AB, CD cut one another in the pt. c „ E ; then the Z AEC shall... | |
 | Euclid, Thomas Tate - 1849 - 120 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...the vertical, or opposite, angles shall be equal. point E ; the angle A EC shall be equal to the angle DEB, and CEB to EAD. angles are together equal... | |
 | Elias Loomis - 1849 - 252 sider
...impossible. Hence BE is not in the same straight line with BC; and in like manner, it may be proved that no other can be in the same straight line with it but BD. Therefore, if at a point, &c. straight line CBE is met by the straight CBD PROPOSITION IV. THEOREM.... | |
 | Royal Military Academy, Woolwich - 1853 - 400 sider
...impossible ; therefore BE is not in the same straight line with BC. And, in like manner, it may he demonstrated, that no other can be in the same straight...same straight line with CB. Wherefore, if at a point, etc. QED PROPOSITION XV. THEOR. If two straight lines cut one another, the vertical or opposite, angles... | |
 | Euclides - 1853 - 176 sider
...greater, which is impossible ; therefore be is not in the same straight line with b С. And in like manner it may be demonstrated, that no other can be in the...which therefore is in the same straight line with С b. Wherefore, if at a point, &c. QED PROPOSITION XV. — THEOREM. If two straight lines cut one... | |
 | Euclides - 1853 - 146 sider
...which is impossible ; therefore 4. 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 6. BD is in the same straight line with CB. Wherefore, if at a point, &c. QED PROP. XV. —... | |
 | Euclides - 1855 - 270 sider
...a right angle with it, these two straight lines shall coincide with each other. PROP. XV. THEOREM. If two straight lines cut one another, the vertical, or opposite angles are equal. Let the two straight lines AB, СD, cut one another in the point E. The angle AEС is equal... | |
 | Cambridge univ, exam. papers - 1856 - 200 sider
...9—12. FIRST DIVISION (A.) 1. To describe an equilateral triangle on a given finite straight line. 2. If two straight lines cut one another, the vertical, or opposite, angles shall be equal. If four straight lines meet in a point, so that the opposite angles are equal, these straight lines... | |
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ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. 
