 | Euclides - 1877 - 58 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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... | |
 | Euclides - 1879 - 146 pagina’s
...therefore is in the same st line with CB. Therefore, if at a point, &c. QE D, PROPOSITION XV. THEOREM. If two straight lines cut one another, the vertical, or opposite angles shall be equal. Let the two st. lines AB, CD cut one another at E. Then shall L AEC = L DEB, and Z CEB = L AED. C* Dem. v AE makes... | |
 | Annie Edwards - 1879 - 514 pagina’s
...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... | |
 | W J. Dickinson - 1879 - 44 pagina’s
...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 pagina’s
...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... | |
 | Moffatt and Paige - 1879 - 428 pagina’s
...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,... | |
 | Joseph Wollman - 1879 - 120 pagina’s
...angles fill the same space. All equal angles fill equal spaces, and not the same space. SECTION II. 1. If two straight lines cut one another, the vertical or opposite angles will be equal. Two equal perpendiculars, PA, QB, are drawn to the line AB from points P, Q, on opposite... | |
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ABD, the less to the 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, which therefore is in the same straight... 
