| Woolwich roy. military acad - 1884 - 148 pages
...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.** 5. Describe a square that shall be equal to a given rectilineal figure. Divide a given straight line... | |
| Stewart W. and co - 1884 - 146 pages
...respectively, then PR and liV are respectively parallel to straight lines KM. and MN. QED SliCTION III. 1. (a) **Triangles upon the same base and between the same parallels are equal.** (b.) Construct a triangle equal to a given triangle and having a base three times as great (a) See... | |
| Euclides - 1884 - 214 pages
...Therefore, the opposite sides &c. Proved. I. 4. E. r. PROPOSITION XXXV. THEOREM. Parallelograms on the **same base, and between the same parallels, are equal to one another.** GIVEN that the parallelograms ABCD and EBCF are on the same base BC, and between the same parallels... | |
| E. J. Brooksmith - Mathematics - 1889 - 354 pages
...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 - 538 pages
...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 - Euclid's Elements - 1891 - 102 pages
...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, John Bascombe Lock - Euclid's Elements - 1892 - 184 pages
...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 - 362 pages
...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 - American periodicals - 1899 - 646 pages
...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... | |
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