| 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 - 356 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 - 188 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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