| Euclid - Geometry - 1890 - 442 pages
...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 pages
...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... | |
| Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...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.... | |
| James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...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... | |
| Peter Alexander - Thermodynamics - 1892 - 228 pages
...are 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 pages
...+ 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... | |
| Northwest Territories Council of Public Instruction - 1897 - 628 pages
...(i) with no pair parallel ; (ii) with one pair parallel ; (iii) with two pairs parallel. (J) Prove **that parallelograms on the same base and between the same parallels are equal** in area. I. 35. (f) Point out the uses of proposition (I) in mensuration. (d) Prove that if a square... | |
| Alfred John Pearce - 1897 - 202 pages
...parallelogram, the length and perpendicular height being given. , Let ABCD be an oblique parallelogram. Now, **parallelograms on the same base and between the same parallels are equal** (Euc. I. 35). Therefore the area of the oblique parallelogram ABCD equals the area of the rectangle... | |
| American Association for the Advancement of Science - Science - 1899 - 650 pages
...geometry, and in the 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... | |
| American Association for the Advancement of Science - American periodicals - 1899 - 646 pages
...geometry, and in the 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 not show that the parallelograms can be divided into pairs of pieces admitting... | |
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