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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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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 pages
...the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. PHOP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC and between the same parallels AD, BC : The EADF triangle...
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Proceedings of the American Association for the Advancement of ..., Volume 48

American Association for the Advancement of Science - Science - 1899
...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 of superposition...
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Transactions of the Cambridge Philosophical Society..

Cambridge Philosophical Society - Science - 1849
...understood, and the proof being gone through, the truth of the proposition must be assented to. That parallelograms upon the same base and between the same parallels are equal; — that angles in the same segment are equal ; — these are propositions which we learn to be true...
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Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850
...MENSURATION, AND TRIGONOMETRY. (Not more than one Question to be answered in each Section.) Section 1. 2. Parallelograms upon the same base, and between the same parallels, are equal. 1. When two straight lines intersect, the opposite anples are equal. . 3. J n an obtuse angled triangle,...
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Papers for the schoolmaster, Volumes 1-6

...advantages the towns possess in being situated as they are. EUCLID AND MECHANICS. First Year Student*. 1. Parallelograms upon the same base and between the same parallels are equal to one another, 2. If a straight line be divided into any two parts, the squares of the whol« line, and of one of...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...and the Proposition should be proved from it.] AEDH XXXV. 1. BOOK I. PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be upon'the same base BC, and between the same parallels AD, BC : E The triangle...
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The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...equal, the parallelogram is divided into two equal parts by the diagonal в c. WWD PBOP. XXXV. THEOB. Parallelograms upon the same base and between the same parallels, are equal. Let the parallelograms ABCDandEBCF, be on the same base в c, and between the same parallels AF and...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...is equal (1 Ax.) to EFGH. "Wherefore parallelograms, etc. QED PROPOSITION XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC : the triangle ABC...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. QED PROP. XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBC, be upon the same base BC and between the same parallels AD, BC. The triangle ABC...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...equal to efgh. Wherefore parallelograms, &c. QED PROPOSITION XXXVII. — THEOREM. Triangles upon tlie same base, and between the same parallels, are equal to one another. LET 'the triangles abС, dbС, be upon the same base bС and between the same parallels ad, bc The triangle...
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