 | John Playfair - Geometry - 1836 - 148 pages
...angles which GH makes with CD, are equal to the corresponding angles which it makes with AB. Therefore, if a straight line, falling on two other straight lines, makes the corresponding angles equal, any other straight line falling on these two straight lines, will also... | |
 | Āryabhaṭa - 1878 - 100 pages
...greater than the angle ABC. Therefore, if one side, &o. QED ' PllOP. VII. THEOREM. (E. 1. 27). jff a straight line falling on two other straight lines, makes the . alternate angles eqtial to each other ; thess two straight lines are parallel, and conversely, if a straight line falls... | |
 | Moffatt and Paige - 1879 - 378 pages
...rectilineal angle. The three lines which bisect the angles of an equilateral triangle meet in a point. 3. If a straight line falling on two other straight lines makes the alternate angles equal to one another, these two straight lines will be parallel. A line drawn through the vertex of an isosceles... | |
 | Moffatt and Paige - 1879 - 474 pages
...? give a list of the necessary signs. GEOMETRY. EUCLID. BOOK I (27-48). Proposition XXVII. Theorem. If a straight line falling on two other straight lines makes the alternate angles equal to one another, these two straight lines shall be parallel. Let the straight line EF, which falls on... | |
 | John Gibson - 1881 - 302 pages
...equal to three given straight lines. This is the twenty-second proposition of the First Book. III. If a straight line falling on two other straight lines,...equal, these two straight lines shall be parallel. This is the twenty -seventh proposition. IV. Describe a parallelogram which shall bo equal to a given... | |
 | John Gibson - 1881 - 64 pages
...shall be equal each to each, and the third angle of the one equal to the third angle of the other. 2. If a straight line falling on two other straight lines makes the alternate angles equal to one another, the two straight lines shall be parallel. 3. Straight lines that are parallel to the... | |
 | Education, Higher - 1884 - 538 pages
...— 8 inclusive. Senior Work, Nos. 5 — 12 inclusive. Higher Local Work, Nos. 9 — 16 inclusive. 1. If a straight line falling on two other straight lines makes the alternate angles equal to one another, the two lines are parallel. 2. Parallelograms on equal bases and between the same parallels... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...extending the sphere of such government, illustrating by concrete cases ? Logic. Women (Pass). 1. " If a straight line falling on two other straight lines...equal, these two straight lines shall be parallel." What inferences can be drawn from this proposition ? 2. Give examples of hypothetical and disjunctive... | |
 | Marianne Nops - 1882 - 278 pages
...27. After this preface we can discuss the first theorem of the division, which tells us that 'when a straight line falling on two other straight lines makes the alternate angles equal, these two lines shall be parallel to each other.' This is proved by the indirect method. Let AB and CD be two... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...taken in BC produced (in the direction B to C) ; show that Q is nearer to A than it is to B. (14.) 9. If a straight line falling on two other straight lines makes the interior angles on the same side together equal to two right angles, the two straight lines are parallel... | |
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Euclid easily proves that if a straight line falling on two other straight lines makes the alternate angles equal to each other, the two straight lines will not meet but are parallel. 
