| James Martineau - 1885 - 539 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... | |
| Nathaniel Bowditch - 1888 - 647 páginas
...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).... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 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 - 400 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 - 231 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
...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
...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
...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 - 79 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.... | |
| Noah Knowles Davis - 1893 - 208 páginas
...quantity, treats almost exclusively of such abstract generalities; as 6=2x3; a?—y' = (x+y) (x—y); **Triangles on the same base, and between the same parallels, are equal.** § 128. Inference in the quantitative whole is immediate and mediate. Immediate inference from equivalent... | |
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