 | Marianne Nops - 1882 - 278 pages
...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 - 176 pages
...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 - Euclid's Elements - 1883 - 428 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 - 568 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 - 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... | |
 | Canada. Department of the Interior - 1888 - 756 pages
...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 - Surveying - 1889 - 306 pages
...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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Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles. 
