| Marianne Nops - 1882
...s GHD, BGH = two rfc. Z s. Wherefore if a straight line, &c. — QED PROPOSITION XXX., THEOREM 21. **Straight lines which are parallel to the same straight line are parallel to** each other. Let AB, CD be each of them || to EF ; AB shall be || to CD. Draw the straight line LM cutting... | |
| Euclides - 1883 - 96 páginas
...meeting 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 - 1883 - 400 páginas
...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
...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 - 1883 - 94 páginas
...*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
...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,... | |
| Henry Elmer Moseley - 1884 - 187 páginas
...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... | |
| Euclides - 1884
...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... | |
| Canada. Department of the Interior - 1888
...every triangle is subtended by the greater side, or, has the greater side oppdsite to it. 2. Show that **straight lines which are parallel to the same straight line are parallel to** each other. 3. Show that if a straight line be divided into two equal parts, and also into two unequal... | |
| George William Usill - 1889 - 272 páginas
...one another, and also the exterior angle equal to the interior and opposite upon the same side. 17. **Straight lines which are parallel to the same straight line are parallel to one another.** 18. If a side of any triangle B c be produced to D, the exterior angle is equal to the two interior... | |
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