| E. J. Brooksmith - 1889
...this proposition. How many of the exterior angles of any triangle must be obtuse ? 4. Parallelograms **upon the same base, and between the same parallels, are equal to one another.** Of all triangles that can be drawn upon a given base and between the same parallels, shew that an isosceles... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 Seiten
...that 'the three medians of a triangle are concurrent.' PROPOSITION 35. THEOREM. Parallelograms on the **same base and between the same parallels are equal to one another. Let** ||gms A BCD, EBCF be on the same base and between the same ||s AF, BC, ABCD shall be equal to EBCF.... | |
| Rupert Deakin - 1891 - 79 Seiten
...the diameter bisects the parallelogram, ie divides it into two equal parts. 35. Parallelograms on the **same base and between the same parallels are equal to one another.** 36. Parallelograms on equal bases and between the same parallels are equal to one another. 37. Triangles... | |
| Euclid - 1892 - 518 Seiten
...PROPOSITION 37. THEOREM. Triangles on the same base, and between the sanie parallels, are equal in area. **Let the triangles ABC, DBC be upon the same base BC, and between the same parallels** BC, AD. Then shall the triangle ABC be equal to the triangle DBC. Construction. Through B draw BE parallel... | |
| Euclid, John Bascombe Lock - 1892 - 167 Seiten
...of equal area. 6. Rectangles having two adjacent sides equal are of equal area. Proposition 37. 139. **Triangles upon the same base and between the same parallels are equal,** Let ABC, DBC represent triangles upon the same base BC and between the same parallels AD, BC ; it is... | |
| Seymour Eaton - 1899 - 340 Seiten
...ABC is equal to the triangle BCD (Proposition 4). PROPOSITION 35. THEOREM 323 Parallelograms on the **same base and between the same parallels are equal to one another. Let the** parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC; then the parallelogram... | |
| American Association for the Advancement of Science - 1899
...part a strict treatment of equivalence. Even Euclid, in proving his I. 35, " Parallelograms on the **same base, and between the same parallels, are equal to one another,"** does not show that the parallelograms can be divided into pairs of pieces admitting of superposition... | |
| American Association for the Advancement of Science - 1899
...third part a strict treatment of equivalence. Even Euclid, in proving his I. 35, "Parallelograms on the **same base, and between the same parallels, are equal to one another,"** does notshowthat the parallelograms can be divided into pairs of pieces admitting of superposition... | |
| Sidney Herbert Wells - 1900
...irregular figure to a triangle of equal area. The principle of this reduction depends upon the fact that **triangles upon the same base and between the same parallels are equal** (Euclid, i., 37), and the method consists of converting certain triangles, obtained from the figure,... | |
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