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" PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 36
by Euclid, James Thomson - 1837 - 390 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...sum of any two adjacent angles of a parallelogram is equal to two right angles. PROP. XXXV. THEOR. Parallelograms upon, the same base and between the same parallels, are equal to one another. > (SEE THE 2d AND 3d FIGURES.) 34 If the sides AD, DF of the parallelograms ABCD, DBCF opposite to...
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A course of practical geometry for mechanics

W. PEASE - 1846
...isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...p. 9, 10; (4), def. above ; (c), def. 16; (d),p.27; ( c) ,p. 32; (/), p. 26. 35 Th. Parallelograms upon the same base (BC), and between the same parallels (AF, BC), are equal to one another. To make ABCD, BCFD, distinct parallelograms on the same base, AF must be...
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The First Book of Euclid's Elements, Simplified, Explained, and Illustrated ...

Euclides - 1847
...from the rt. L to the pt. of bisection is = to half the hypothenuse. PROP. XXXV. THEOR. GEN. ENUN. — .Parallelograms upon the same base, and between the same parallels, are equal to one another. PART. ENUN. — Let the a ms ABCD, EBCF (Fig. 2 and 3) be upon the same base BC, and between the same...
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THE SOLUTIONS OF GEOMETRICAL PROBLEMS

THOMAS GASKIN, M.A., - 1847
...Geometry. TG CAMBRIDGE, Nov. 1847. GEOMETRICAL PROBLEMS. ST JOHN'S COLLEGE. DEC. 1830. (No. I.) 1. PARALLELOGRAMS upon the same base and between the same parallels are equal to one another. 2. Of unequal magnitudes,, the greater has a greater ratio to the same than the less. 3. If the diameter...
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The Philosophy of the Inductive Sciences: Founded Upon Their History, Volume 1

William Whewell - Science - 1847
...contingent truths. The former kind are Truths which cannot but be true; as that 19 and 11 make 30 ; — that parallelograms upon the same base and between the same parallels are equal: — that all the angles in the same segment of a circle are equal. The latter are Truths which it happens...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...lines ; and point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Show hence that the area of a parallelogram is properly measured by the product of the numbers that...
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Report of the Committee of Council on Education (England and Wales ..., Issue 2

Great Britain. Council on Education - Education - 1848
...lines ; and point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that...
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Minutes of the Committee of Council on Education, with Appendices, Volume 2

Great Britain. Committee on Education - 1848
...lines ; and point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...another, and the diameter bisects them, that is, divides them into two equal parts. PROP. XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. PROP. XXXVI. THEOREM. PROP. XXXVII. THEOREM. Triangles upon the same base anti between the same parallels,...
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