 | Education Department,London - 1876 - 1010 sider
...from points P,Q, on opposite sides of AB ; AB is bisected in O. Show that POQ is a straight line. 1. If two straight lines cut one another, the vertical or opposite angles will be equal. БЛС is a right angled triangle, right angled at A ; CD is drawn to any point D of... | |
 | Euclides - 1877 - 58 sider
...angla AEC greater than the angle BED ; then CED cannot be a straight line. PROPOSITION XV. THEOREM. If two straight lines cut one another, the vertical...shall be equal. Let the two straight lines AB, CD cut each other in the point E ; then shall the angle AEC be equal to the angle BED, and the angle AED to... | |
 | Edward Atkins - 1877 - 72 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 same straight line with it but BD. Therefore BD is in the same straight line with EG. Therefore, if at a point, <tc. QED Proposition 15.... | |
 | Elias Loomis - 1877 - 458 sider
...the greater, which is absurd. Therefore two straight lines which have, etc. PROPOSITION V. THEOREM. If two straight lines cut one another, the vertical or opposite angles are equal. Let the two straight lines AB, CD cut one another in the point E ; then will the angle AEC... | |
 | Āryabhaṭa - 1878 - 100 sider
...circlet cut one another, they have not the same centre (Prop. 6 : 3. E.). PBOP. II. (Prop. 15. Book IE) If two straight lines cut one another, the vertical or opposite angles are equal. Let the straight lines AC and 151) cut one another at tho point F. The vertical or opposite... | |
 | Moffatt and Paige - 1879 - 428 sider
...greater, which is impossible. Therefore BE is not in the same straight line with B C. In the same way it may be demonstrated that no other can be in the same straight line with it but B D. Therefore BD is in the same straight line with B C. Therefore, if, at a point in a straight line,... | |
 | W J. Dickinson - 1879 - 44 sider
...to two right angles ; then these two straight lines shall be in one and the same straight line. 15. If two straight lines cut one another, the vertical, or opposite angles shall be equal. Deduce from this, that all the angles made by any number of straight lines meeting in one point are... | |
 | Edward Harri Mathews - 1879 - 94 sider
...other : and if the equal sides be produced, the angles on the other side of the base shall be equal. 3. If two straight lines cut one another, the vertical or opposite angles shall be equal. Deduce clearly from this and preceding propositions that all the angles made by any number of straight... | |
 | Annie Edwards - 1879 - 514 sider
...Jeanne picks up her lesson-book, ' Euclid's Elements,' from the ground. " ' Proposition XV. Theorem. If two straight lines cut one another, the vertical, or opposite, angles shall be equal.' Then why try to prove it ? Why need we go on with these hideous angles and right angles? Why do you... | |
 | Euclides - 1879 - 146 sider
...= the greater, which is impossible ; /. BE is not in the same st. line with CB. And in the same way it may be demonstrated, that no other can be in the same st. line with it but BD, which therefore is in the same st line with CB. Therefore, if at a point,... | |
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ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. 
