| United States. Congress. Senate - 1880
...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 - Liczba stron: 539
...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 - 1888 - Liczba stron: 647
...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 - 1890 - Liczba stron: 400
...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 - Liczba stron: 515
...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... | |
| Dalhousie University - 1891
...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... | |
| Thomas Baker - 1891 - Liczba stron: 231
...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... | |
| James Andrew Blaikie, William Thomson - 1891
...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... | |
| 1891
...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... | |
| Rupert Deakin - 1891 - Liczba stron: 79
...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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