| Education Ministry of - 1882 - 302 pages
...a greater angle. Write out the enunciations of any previous propositions employed in this proof. 3. **Straight lines, which are parallel to the same straight line, are parallel to** each obher. If two adjacent sides of a parallelogram be parallel to two adjacent sides of another parallelogram,... | |
| Euclides - 1883 - 176 pages
...AB at E. Prove that EDB is an isosceles triangle. For Euclid I. 30, see Appendix. PROP. 30. THEOR. **Straight lines which are parallel to the same straight line are parallel to one another.** Given AB || CD, and EF || AB CD. To prove AB || EF. s If AB is not || EF, they will EF meet; then there... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...Therefore the angles BGH, GHD are together equal to two right angles. [Axiom 1. PROPOSITION 30. THEOREM. **Straight lines which are parallel to the same straight line are parallel to** each other. Let AB, CD be each of them parallel to EF: AB shall be parallel to CD. Let the straight... | |
| 1886 - 564 pages
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 4. **Straight lines which are parallel to the same straight line are parallel to** each other. 5. To divide a given straight line into two parts, so that the rectangle contained by the... | |
| J. McD. Scott - Metaphysics - 1883 - 104 pages
...*less than two right angles. Neither postulate nor axiom is needed but once ; namely, to prove that **lines which are parallel to the same straight line are parallel to** each other. It matters not which we use, for -by either we can prove the other. The real problem is... | |
| Euclides - 1884 - 182 pages
...on opposite aides of HC ; then show that AB and CD are parallel. 72. PROPOSITION XXX. — THEOREM. **Straight lines which are parallel to the same straight line are parallel to one another.** Let the straight lines AB, CD be each of them parallel ioEF. Then shall AB be also parallel to CD.... | |
| Euclides - 1884 - 434 pages
...draw DE _L AC, and meeting CB at E. From E draw EF _L DE and = EC; join CF. PROPOSITION 30. THEOREM. **Straight lines which are parallel to the same straight line are parallel to one another.** AB CD Let AB and CD be each of them || EF: it is required to prove AB \\ CD. If AB and CD be not parallel,... | |
| Euclides - 1884 - 214 pages
...equal to two right angles. Axiom 1. Therefore, if a straight line &o. QED PROPOSITION XXX. THEOREM. **Straight lines which are parallel to the same straight line are parallel to** each other. GIVEN that AB ami CD are each parallel to EF; 11 IS REQUIRED TO PROVE that AB is parallel... | |
| Henry Elmer Moseley - Universities and colleges - 1884 - 214 pages
...2. Prove that the angles at the base of an isosceles triangle are equal to each other. 3. Prove that **straight lines which are parallel to the same straight line are parallel to** each other. 4. Prove that the diagonals of a parallelogram bisect each other. 5. Inseribe a trapezium... | |
| Mathematical association - 1884 - 146 pages
...first pair are respectively equal to the angles made by the second pair. THEOK. 24. Straight lines that **are parallel to the same straight line are parallel to one another.** Let the straight lines AB, CD be each parallel to the straight line EF : A a c_ p then shall AB and... | |
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