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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Examination Papers for Science Schools and Classes - Page 23
by Great Britain. Education Department. Department of Science and Art - 1882
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The Oxford examiner, ed. by M.W.I. Shilleto, Issues 1-5

Mary W I. Shilleto - 1882 - 418 pages
...students are advised not to confine themselves to one paper, but to make use of the whole set. (a) 1. Parallelograms on the same base and between the same parallels are equal. AOC is an isosceles triangle, of which A is the vertex : AB, AC are bisected in D & E respectively...
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 176 pages
...the figure is a parallelogram. On Equality of Area of certain Rectilineal Figures. PROP. 35. THEOR. Parallelograms on the same base and between the same parallels are equal to one another. Fie. 1. FIG. 2. Fio. 8. ADEADEFAED In Fig. 1, Let ABCD, DBCE be the parallelograms...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...4. and the diameter BG divides the parallelogram AGDB into two equal parts. PROPOSITION 85. THEOREM. 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 sameparallels...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...difference of identically equal magnitudes are equal, although they may not be identically equal. THEOR. 1. Parallelograms on the same base and between the same parallels are equal. COR. 1. A parallelogram is equal to a rectangle, whose base and altitude are equal to those of the...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...triangle ABC, 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...right-angled at C ; draw CD at right angles to AB; in CD take CE equal to BD, and in CA take CF equal to AD ; join AE and BF; and show that AE and BFsie...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...16. Construct a triangle, having given the middle points of its three sides. PROPOSITION 35. THEOREM. Parallelograms on the same base and between the same parallels are equal in area. ADEFAEDF BO BO Let ABCD, EBCF be ||ms on the same base BC, and between the same parallels...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...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...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...differences of identically equal magnitudes are equal, although they may not be identically equal. THEOR. I. Parallelograms on the same base and between the same parallels are equal. Let ABCD, EBCF be two parallelograms on the same base EC, and between the same parallels AF, BC : \*:...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...differences of identically equal magnitudes are equal, although they may not be identically equal. THEOR. I. Parallelograms on the same base and between the same parallels are equal. Let ABCD, EBCF be two parallelograms on the same base EC, and between the same parallels AF, BC : then...
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885 - 652 pages
...line perpendicular to a given straight line of unlimited length, from a given point without it. 3. Parallelograms on the same base, and between the same parallels, are equal to one another. 4. If a straight line be divided into two equal parts and also into two unequal parts,...
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