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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

Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844 - 456 pages
...its central length is 21 f. 5 i. ; What is the quantity of wood in cubic yards ? 1843. GEOMETRY. 2. Parallelograms on the same base, and between the same parallels are equal. 3. If in a circle two chords eat one another, prove that the rectangle contained by the segments of...

The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
.... . II '. . JUNIOR MODERATOR AND SENIOR EXAMINER. [The Differential Calculut it not to be wed.] 1 . Parallelograms on the same base and between the same parallels are equal to one another. 2. From a given circle to cut off a segment containing an angle equal to a given rectilineal...

The Philosophy of the Inductive Sciences: Founded Upon Their History, Volume 2

William Whewell - History - 1847 - 716 pages
...himself with the first twenty-six propositions of Euclid, and not till then, it becomes evident to him, that parallelograms on the same base and between the same parallels are equal ^ and he cannot even conceive the contrary. When he has a little further cultivated his geometrical...

The examinations for the degree of bachelor of arts, Jan., 1847

Cambridge univ, exam. papers - 1847 - 40 pages
...and x both lie between 0 and 1, prove that >x. i — a 3. In the figure of Euclid, Book i. Prop. 35, (Parallelograms on the same base and between the same parallels are equal,) if two diagonals be drawn to the two parallelograms respectively, one from each extremity of the base,...

Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...angles, or 180°; if two be known, they must be deducted from 180°, to leave the third. 2. " Prove that parallelograms on the same base and between the same parallels are equal to one another." Euclid i. 35. Tate, Art. 48. 3. " In any right-angled triangle the square which js...

Proceedings of the American Association for the Advancement of ..., Volume 48

American Association for the Advancement of Science - Science - 1899 - 648 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...

An elementary course of practical mathematics, Part 2

James Elliot - 1851 - 152 pages
...any scale : inscribe a circle in it, and circumscribe a circle about it. PROPOSITION LVI. THEOREM. Parallelograms on the same Base and between the same Parallels are equal. Let the two parallelograms ABCD and CDEF stand on the same base CD, and have their sides opposite CD...

Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...rectangles of their containing sides (AB-BC and DE'EF). Draw AG, DH, perpendiculars to BC, EF. Then because parallelograms on the same base and between the same parallels are equal, AC=AG'BC, and DF=DH-EF. Also the rectangles AG-BC, AB-BC having the same altitude BC, are to each other...