 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...angles; and the three interior angles of every triangle are together equal to two right angles. 4. Equal triangles upon the same base and upon the same side of it, are between the same parallels. A line drawn through the middle points of two sides of a triangle, will be parallel to the third side.... | |
 | 1855 - 264 pages
...angles of every triangle are together equal to two right angles. 4. Equal triangles upon the same hase and upon the same side of it are between the same parallels . A. line drawn through the middle points of two sides of a triangle will be parallel to the third... | |
 | Euclides - 1856 - 168 pages
...point G will coincide with F, and the line EG with EF; wherefore EG or BC is equal to E F. XLII. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBG (Fig. 33) be upon the same base BC, and upon the same side of it ;... | |
 | 1857 - 400 pages
...equal to a given triangle, and having an angle equal to a given rectilineal angle. Quest. 2. Equal triangles upon the same base and upon the same side of it, are between the same parallels. Quest. 3. If one side of a triangle be produced, the exterior angle is greater than either of the interior... | |
 | Euclides - 1858 - 248 pages
...the triangle AB ( ' has been bisected from the point H by the line HE. QKF PROP. 39.— TIIEOR. Equal triangles upon the same base and upon the same side of it are between the same parallels. CONSTRUCTION. — Pst. 1. A line may be drawn between two points. 1*. ,-il. Through a given point to... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1859 - 140 pages
...ad absurdum, and illustrate it by Euclid, Book I., Prop. 39, "Equal triangles, upon the same4Sase, and upon the same side of it, are between the same parallels." Is the reducuo adabstirdnmofless force than the direct forms of inference ? 3. Construct an isosceles... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC and upon the same side of it. Then the triangles... | |
 | Euclides - 1861 - 464 pages
...to one another; and those to which the same M has the some R are eq. to one another. 39, 1. Eq. Дs upon the same base and upon the same side of it are between the same parallels. E. l C. Hyp. 1. Cone. C. CASE I. Let DE be [| BC, one of the sides of Д ABC; and let DE cut the other... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...be the diameter of a circle, the circumference of the circle will bisect the base of the triangle. 21. Parallelograms which have two sides and the included...parallels. 23. If the middle points of the sides of a trapezoid, which are not parallel, be joined by a straight line, that line will be parallel to each... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...be the diameter of a circle, the circumference of the circle will bisect the base of the triangle. 21. Parallelograms which have two sides and the included...be parallel to each of the two parallel sides, and be equal to half their sum. 24. If, in opposite sides of a parallelogram, at equal distances from opposite... | |
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Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 
