 | Royal Society of Edinburgh - Science - 1880 - 864 pages
...the va-rtpov irpar«pov of discussing the construction of an equilateral triangle before proving that when two straight lines cut one another the vertically opposite angles are equal ! Appendix on the Trigonometry of Elliptic and Hyperbolic Space. The following appears to me to be... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...number of straight lines that meet in a point, are together equal to four right-angles. 8. Prove that when two straight lines cut one another the vertically opposite angles are equal. 9. Show how to form a square angle. Show how to test a setsquare. 10. Explain how a perpendicular may... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...together equal to two right angles, these two straight lines are in one straight line, THEOR. 4. If two straight lines cut one another, the vertically opposite angles are equal to one another. SECTION 2. TRIANGLES. DEF. 30. An isosceles triangle is that which has two sides equal.... | |
 | Education, Higher - 1882 - 498 pages
...and the sides adjacent to equal angles also equal, the triangles are equal in every respect. 3. If two straight lines cut one another the vertically opposite angles are equal. 4. From a given point draw the shortest line possible to a given straight line. 5. Any two sides of... | |
 | Mathematical association - 1883 - 86 pages
...together equal to two right angles, these two straight lines are in one straight line. THEOR. 4. If two straight lines cut one another, the vertically opposite angles are equal to one another. DEF. 31. A right-angled triangle is that which has one of its angles a right angle.... | |
 | Education - 1892 - 652 pages
...line with two others make two right angles these two lines are in one straight line. 10. Prop. IV. If two straight lines cut one another the vertically opposite angles are equal. Section II. Triangles. 11. Prop. V. If a perpendicular is erected at the middle point of a straight... | |
 | Euclid - Geometry - 1890 - 442 pages
...which cannot be, unless AZ lie along AY. .'. XA, AY are in a st. line. Proposition 15. THEOREM — If two straight lines cut one another, the vertically opposite angles are equal. Let the two st. lines AB, CD, cut one another in X. Then, since DX meets AXB, AA . BXD + DXA = two... | |
 | William Whitehead Rupert - Geometry - 1900 - 148 pages
...probability refer back to him : i. The angles at the base of an isosceles triangle are equal. ii. If two straight lines cut one another, the vertically opposite angles are equal. Thales may have regarded this as obvious. Euclid, who was of Greek descent, and who was born about... | |
 | Walter William Rouse Ball - Mathematics - 1901 - 580 pages
...turning it over, and then superposing it on the first ; a sort of experimental demonstration. (ii) If two straight lines cut one another, the vertically opposite angles are equal (Euc. ,, 15). Thales may have regarded this as obvious, for Proclus adds that Euclid was the first... | |
 | Alfred Baker - Geometry - 1903 - 154 pages
...2 rt. angles = ZEBC + ZEBA, and dropping from both sides the angle ABE, we have ZABD=ZEBC. Hence if two straight lines cut one another, the vertically opposite angles are equal. Yet such a proposition scarcely needs demonstration; for, as was said in Chapter I., a straight line... | |
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I., 5), (3) that, if two straight lines cut one another, the vertically opposite angles are equal (Eucl. 
