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" In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... "
The Theory and Practice of Surveying: Containing All the Instructions ... - Página 173
por Robert Gibson - 1832 - 348 páginas
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Calendar, for the Year ...

1894
...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....
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Annual Report

1894
...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...
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Colliery Surveying: A Primer Designed for the Use of Students and Colliery ...

Thomas Aloysius O'Donahue - 1896 - 163 páginas
...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,...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1899
...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...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 páginas
...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...
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Report of the Department of Education for the Year ...

Manitoba. Department of Education - 1900
...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...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Libro 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 páginas
...(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....
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A Text-book of Euclid's Elements for the Use of Schools, Libro 1

Euclid - 1904 - 456 páginas
...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....
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A Manual of Carpentry and Joinery

J. W. Riley - 1905 - 500 páginas
...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...
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A Manual of Carpentry and Joinery

J. W. Riley - 1905 - 500 páginas
...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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