 | Euclides - 1884 - 214 páginas
...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... | |
 | United States. Congress. Senate - 1880 - 1304 páginas
...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 - 1885 - 516 páginas
...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... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 páginas
...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... | |
 | Euclid - 1890 - 442 páginas
...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.... | |
 | Thomas Baker - 1891 - 262 páginas
...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... | |
 | Dalhousie University - 1891 - 136 páginas
...THREE HOURS. 1. Enunciate the propositions of Euclid dealing with the equality of triangles. 2. Prove that triangles on the same base and between the same parallels are equal. 3. If a straight line be divided into two parts, the square on the whole line is equal to the sum of... | |
 | 1891 - 718 páginas
...angle LMN to the angle PQR, also the side MN equal to QR; prove that the side LMis equal to PQ. 2. Triangles on the same base and between the same parallels are equal to one another. 3. In a right-angled triangle the square on the side opposite the right angle is equal... | |
 | James Andrew Blaikie, William Thomson - 1891 - 154 páginas
...the parallelogram. 36. Parallelograms on equal bases and between the same parallels are equal. 37. Triangles on the same base and between the same parallels are equal. 38. Triangles on equal bases and between the same parallels are equal. 39. Equal triangles on the same... | |
 | Rupert Deakin - 1891 - 102 páginas
...another. 36. Parallelograms on equal bases and between the same parallels are equal to one another. 37. Triangles on the same base and between the same parallels are equal to one another. 38. Triangles on equal bases and between the same parallels are equal to one another.... | |
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In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... 
