 | University of Cambridge - 1884 - 624 pages
...other angles shall be equal, each to «*acb. namely tboee to which the equal sides are opposite. 9. Triangles on the same base, and between the same parallels, are equal. In the sides В С, CD of a parallelogram AB С D points P, Q are taken such that PQ i» parallel to BD.... | |
 | Euclides - 1884 - 214 pages
...to the parallelogram EFGH. Axiom 1. Therefore, parallelograms <kc. QED PROPOSITION XXXVII. THEOREM. Triangles on the same base, and between the same parallels, are equal. GIVEN that tlie triangles ABC and DBC are on the same base BC, and between the same parallels AD and... | |
 | London univ, Middlesex hosp. med. sch - 1884 - 28 pages
...864. 8. — Show that the length of the edge of a cube multiplied by \/3 gives its diagonal. 9. — Triangles on the same base and between the same parallels are equal. 10. — If a straight line be divided into two parts, the square of the whole line, minus twice the... | |
 | 1885 - 522 pages
...meet in B. Prove that the angles ABC, ABD are together equal to two right angles. 2. Parallelograms on the same base and between the same parallels are equal in area. 3. Describe a rectangle which shall be equal to a given parallelogram. 4. C is a point in the straight... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...axiom upon which your proof in based, and mention any other which has been proposed instead of it. <• Triangles on the same base and between the same parallels are equal to each other. ¿92 NAVAL EDUCATION — 5. Describe a square which »hall be equal to a given rectilineal... | |
 | James Martineau - Ethics - 1885 - 516 pages
...are the same eternal truths which God sees. For God sees as well as I that twice two are four, and that triangles on the same base and between the same parallels are equal. I can also discover, at least dimly, the relations of perfection among these ideas; and these relations... | |
 | Nathaniel Bowditch - Nautical astronomy - 1888 - 704 pages
...therefore the three parallelograms AUDC, BDFE, and EFHG are equal to each other. Cor. Hence it follows that triangles on the same base and between the same parallels are equal, since they are the half of the parallelograms on the same base and between the same parallels (by XXII).... | |
 | Euclid - Geometry - 1890 - 442 pages
...same ||8; and for similar reasons, a CDRS = a ABRS. .-. a ABPQ = a CDRS. Proposition 37. THEOREM — Triangles on the same base, and between the same parallels, are equal in area. Draw AX j| to BP, and BY || to AQ ; and let them meet PQ, produced both ways, in X and Y respectively.... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...solutions, and to point out the cases in which the full number cannot be obtained. PROPOSITION 37. THEOREM. Triangles on the same base and between the same parallels are equal to one another. Let ABC and DBC be As on the same base BC, and between the same ||s AD and BC, then... | |
 | Thomas Baker - Railroads - 1891 - 262 pages
...purpose is here given. This method is founded on a well-known proposition of Euclid, in which it is shewn that triangles on the same base, and between the same parallels, are equal. Let ABC, ABDbe triangles on the same base AB, and between the same parallels AB, CD; then the triangle... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
