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If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.
Skeleton propositions &c. of Euclid, books i and ii, with references, by H ... - Pagina xl
door Euclides - 1868
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## The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - 1858 - 324 pagina’s
...half a parallelogram upon the same base, and of equal altitude, or between the same parallels ; and " if a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle." A trapezium is an irregular four-sided...
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## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pagina’s
...of any triangle be produced, the extorior angle is equal to the two interior and opposite angbs. k If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogran is double of the triangle. 3. Tf a straight line be divided into two equal...
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## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...equal ; and if the areas and altitudes be equal, the bases are equal. PROPOSITION XLI. THEOREM. . . .,, If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle: Given the parallelogram ABCD and the...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 pagina’s
...AD is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram ABCD, and the...
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## Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...is parallel to BF. Conclusion. — Therefore, equal triangles, &c. QED PROPOSITION 41.— THEORKM. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. (Ref erencea— Prop. I. 34, 37; ax....
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## Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863
...Thus saudre and -"""^-e rooi are corelative terms."— LAEDNER.S Euclid, p. 54. PROP. 41— THEOR. If a parallelogram and a triangle be upon the same base and between the same parallels ; the parallelogram shall be double of the triangle. Cos.— Pst. 1.— DEM.— P. 37, PM...
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## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...AD is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle, Let the parallelogram ABCD, and the...
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## The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...bases in the same straight line, and towards the same parts, are between the same parallels. Prop. 41. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. Prop. 42. To describe a parallelogram...
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## Papers for the schoolmaster, Volume 4

1868
...the least perimeter. 2. Triangles upon the same base, and between the stime parallels, are equal. 3. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. If through the angles of a parallelogram...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pagina’s
...AD is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram ABCD, and the...
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