 | Edward Atkins - 1877 - 72 pages
...Therefore, if two triangles, <kc. QED Proposition 27. — Theorem. If a straight line falling upon two other straight lines make the alternate angles equal to one another, these two straight lines shall be parallel, Let the straight line EF, which / falls upon the two straight... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...Propositions XXVH.-XLI. (inclusive). 27. When are straight lines said to be parallel to one another? Prove that if a straight line falling on two other straight lines make the alternate angles equal to each other, these two straight lines must be parallel. Same proposition. What axiom does Euclid for... | |
 | Edward Harri Mathews - 1879 - 94 pages
...two ends of a given straight line simultaneously describe circles about two different centres? 2. " If a straight line falling on two other straight lines make the alternate angles equal to each other, these two straight lines shall be parallel." What supposition is tacitly assumed concerning... | |
 | Euclides - 1879 - 146 pages
...this line must be either parallel to the base or perpendicular to it. PROPOSITION XXVIII. THEOREM. If a straight line falling on two other straight lines •make the exterior angle equal to the interior and opposite on the same side of the line; or make the interior... | |
 | 1880 - 160 pages
...other, the base of that which has the greater angle shall be greater than the base of the other. 5. If a straight line falling on two other straight lines...two straight lines shall be parallel to one another. 6. Triangles on the same base and between the same parallels are equal. 7. Describe a parallelogram... | |
 | Oxford univ, local exams - 1880 - 396 pages
...double of the square on half the line and of the square on the line between the points of section. 6. If a straight line falling on two other straight lines,...two straight lines shall be parallel to one another. 7. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
 | Alfred Milnes - 1880 - 140 pages
...contradictories to an absurdity. One such proposition we will examine from a logical point of view : — " If a straight line falling on two other straight lines...straight lines shall be parallel to one another." — Euclid, I. 27; Wilson's Geometry, I. 21. Now, this proposition says that, granted certain conditions,... | |
 | Pupil teachers - 1880 - 1486 pages
...Propositions XXVUL-XLI. (inclusive). 27.When are straight lines said to be parallel to one another ? Prove that if a straight line falling on two other straight lines make the alternate angles equal to each other, these two straight lines must be parallel Same proposition. What axiom does Euclid for... | |
 | 1880 - 594 pages
...ridicule, he strolled quietly home, a triumphant Tory. Euclid. — i. What is meant by alternate angles ? If a straight line falling on two other straight lines make the alternate angles equal to each other, these two straight lines shall be parallel. 2. How many sides has a figure if the sum of... | |
 | T S. Taylor - 1880 - 152 pages
...The Enunciations of Euc. I. 13 ; I. 15 ; I. 27 ; and Axioms i, 2, 30, and 10. General Enunciation. If a straight line falling on two other straight lines, make the exterior angle equal to the interior and opposite angle on the same side of the line, or make the interior... | |
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THEOREM. If a straight line falling on two other straight lines, make the exterior angle equal to the interior and opposite... 
