 | 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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Straight lines which are parallel to the same straight line are parallel to one another. 
