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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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First book of mathematics

Hugo Reid - Mathematics - 1872 - 148 pages
...to meet CD or that line produced. 142. If ote. — This illustrates the important geometrical truth, that — Parallelograms on the same base and between the same parallels are equal to one another; that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...which a paral. .am is divided by its diagonals, are equal to each other. PROPOSITION XXXV. THEOREM. Parallelograms on the same base and between the same parallels are equal. Let the OĞ ABCD, EBCF be on the same base BC, and between the same \\aAF, BC. Then must £]ABCD=E]EBCF....
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873 - 182 pages
...the same base and between the same parallels are equal to one another. (10.) (This appears to mean that parallelograms on the same base and between the same parallels are equal, and also that triangles on the same base and between the same parallels are equal. See Geometry, Props....
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...is a parallelogram. 3. The diagonals of a parallelogram bisect each other. PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. .. Let the parallelograms ABCD, EBCFbe on the '• same base BC, and between the same...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...(i. 27) the O ^^T is both equilateral and rectangular, and is .-. a square. AREAS. PROPOSITION XXXI. Parallelograms on the same base and between the same parallels are equal. TJ E -BC Let the O s A BCD, EBCF be on the same base BC, and between the same parallels AF, BC. Then...
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...straight line perpendicular to a given straight line of unlimited length from a given point without it. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. If a straight line be bisected, and produced to any point, the rectangle contained...
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The elementary geometry of the right line and circle

William Alexander Willock - Circle - 1875 - 196 pages
...parallelograms OQt and O,Q, which are the complementary parallelograms, are (Ax. 3) equal in area, as stated. 6. Parallelograms on the Same Base and between the Same Parallels are equal in area. Bl Ot Let AB be the common base, and ABA.B, and ABA B2 two such parallelograms on AB and between...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...difference 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. COR. i. The area of a parallelogram is equal to the area of a rectangle, whose base and altitude are...
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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...opposite angle on the same side of the line, the two straight lines shall be parallel to one another. 2. Parallelograms on the same base and between the same parallels are equal to each other. If the angular points of two equal parallelograms which stand on the same base but on...
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Report of the Secretary for Public Instruction ..., Volume 33

Queensland. Department of Public Instruction - Education - 1909 - 144 pages
...equal to three given straight lines, any two of which are together greater than the third. 4. Prove that parallelograms on the same base and between the same parallels are equal. 5. Prove that if a straight line lie divided into two parts, the squares on the whole line and on one...
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