 | 1894 - 1136 sider
...triangle which has the greater contained angle shall be greater than the base of the other. I. 24. 8. Triangles on the same base and between the same parallels are equal in area. I. 37. 9 To describe a parallelogram equal to any given rectilineal figure, and having an... | |
 | Thomas Aloysius O'Donahue - 1896 - 186 sider
...method of casting out areas is that known as " equalising," which is based on Euclid's proposition of " triangles on the same base and between the same parallels are equal." The method consists in constructing a triangle equal to the figure, the area of which is required,... | |
 | Great Britain. Education Department. Department of Science and Art - 1899 - 348 sider
...rectilineal figure equals seven-eighths of two right angles, find the number of sides. (12.) 10. Show that triangles on the same base and between the same parallels are equal in area. ABCD is a parallelogram, and P is a point within the angle formed by DC and the prolongation... | |
 | Seymour Eaton - 1899 - 362 sider
...EBCH. Therefore the parallelogram ABCD is equal to the parallelogram EFQII. PROPOSITION 37. THEOREM Triangles on the same base, and between the same parallels, are equal. Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD, BC ; then the... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 330 sider
...(ii) Parallelograms on equal bases and of equal altitudes are equal in area. PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal in area. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels BC, AD.... | |
 | Manitoba. Department of Education - 1900 - 558 sider
...drawn from two angles of a triangle and terminated by the opposite sides can bisect one another. 4. Two .triangles on the same base and between the same parallels are equal. By means of this proposition show how to describe a triangle equal to a given quadrilateral ; and Bisect... | |
 | Euclid - 1904 - 488 sider
...parallelogram is equal in area to a rectangle of equal base and equal altitude. PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal in area. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels BC, AD.... | |
 | J. W. Riley - 1905 - 522 sider
...work it graphically, finding a rectangle of equal area. This is done by an application of the fact that triangles on the same base and between the same parallels are equal in area (Fig. 157, p. 93). Produce AB and join AD. Through E draw EF parallel to DA ; then the triangles... | |
 | J. W. Riley - 1905 - 518 sider
...height area = base xr — c S— . 2i The shape of the triangle does not affect the result, as all triangles on the same base and between the same parallels are equal in area. The area of a triangle can also be determined by the following formula : \^s(s - a)(s - b)(x... | |
 | Joseph Gregory Horner - 1909 - 560 sider
...angles; and the three interior angles of every triangle are equal to two right angles. (Prop. 32.) Triangles on the same base and between the same parallels are equal to one another. (Prop. 37.) Triangles on equal bases and between the same parallels are equal to one... | |
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In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... 
