 | Euclides - 1884 - 182 ページ
...cutting AB in D and AC in E, so that DE shall be equal to the sum of BD and CE. (14) 1 1 . Show that parallelograms on the same base and between the same parallels are equal. Show how to construct an isosceles triangle equal to a given triangle. (10) 12. ABC is a triangle right-angled... | |
 | Euclides - 1884 - 214 ページ
...parallelogram ACDB. 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... | |
 | Euclid - 1890 - 442 ページ
...quadrilateral is a parallelogram if its diagonals bisect each other. 39 Proposition 35. THEOREM — Parallelograms on the same base, and between the same parallels, are equal in area. Q CO (2) SP RQ SP R (.3) PS B B Let ABPQ, ABRS be on same base AB, and between same \\s AB,... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 ページ
...be concurrent. Note 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... | |
 | Thomas Baker - 1891 - 262 ページ
...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 - 160 ページ
...and opposite angles of a parallelogram are equal, and either diagonal bisects the parallelogram. 35. Parallelograms on the same base and between the same parallels are equal. 36. Parallelograms on equal bases and between the same parallels are equal. 37. Triangles on the same... | |
 | Rupert Deakin - 1891 - 102 ページ
...to one another, and 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.... | |
 | Peter Alexander - 1892 - 228 ページ
...parallel to OX, and the lines hX', kN, Eu, L8, Da, PJTare parallel to OF. From Euclid's theorem that parallelograms on the same base and between the same parallels are equal, we get ASCD = AKQD = AKPk = AH . Ak, = ABUL = AISL =AL . Al, = AMWD = AMRm = AM. Am, = ABX'N= An VN... | |
 | University College, Galway - 1896 - 430 ページ
...+ x by a? - x + 1. 5' Simplify (*+l)H (*-!)». 6. Solve the equation x + 5 x - 6 x + 3 ~ x - 9' 7. Parallelograms on the same base and between the same parallels are equal in area. 8. If a straight line is bisected and also divided unequally the sum of the squares on the... | |
| |
Prove that parallelograms on the same base and between the same parallels are equal in area. 
