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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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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 1

Euclides - 1868
...5 Def. A. 6 D. 5. H. 7 P. 35. 8 P. 85. 9 Ax. 1. 10 Becap. • PilOP. XXXVII. Тикоа. Triangles upon the same base and between the same parallels are equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon...
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History of Scientific Ideas, Part 1

William Whewell - Knowledge, Theory of - 1858
...contingent truths. The former kind are Truths which cannot but be true; as that 19 and n 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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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...four-sided figures of which the opposite sides are parallel ; . . BGHA & BPKD are parallelograms. ix. Parallelograms upon the same base and between the same parallels, are equal : x. EBAF and BGHA are parallelograms on the same base, &c. ; .'. EBAF and BGHA are equal parallelograms....
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...the greater angle shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. If a straight line be divided into any two parts, the squares of the whole line and of one of the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...EFGH. (ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. T•iangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, D-BCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle...
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Cambridge senate-house problems and riders for the year 1860; with solutions ...

Henry William Watson - 1860
...and for the rectangle contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860
...lines make the alternate angles equal to each other, these two straight lines shall be parallel. 5. Parallelograms upon the same base and between the same parallels are equal to one another. The perimeter of a square is less than that of any other parallelogram of equal area. 6. If a straight...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...; therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 317 pages
...same EBCH : Therefore also the parallelogram ABOI? it «qual to EFGH. PROP. XXXVII. THEOR. Trim gles upon the same base, and between the same parallels, are equal to ont another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD,...
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On the Philosophy of Discovery: Chapters Historical and Critical

William Whewell - Philosophy - 1860 - 531 pages
...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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