 | 1894 - 278 σελίδες
...described ? In what proposition does Euclid imply the fact that there can be more than one ? 2. Prove that triangles on the same base and between the same parallels are equal to each other. Through a given point in the base of a triangle draw a straight line bisecting the triangle.... | |
 | 1894 - 1136 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Manitoba. Department of Education - 1900 - 558 σελίδες
...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, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 330 σελίδες
...(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.... | |
 | Euclid - 1904 - 488 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
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In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... 
