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" ... that triangles on the same base and between the same parallels are equal... "
A Treatise of Practical Surveying: Which is Demonstrated from Its First ... - Strona 207
autor: Robert Gibson - 1806 - Liczba stron: 452
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...appears to mean that parallelograms on the same base and between the same parallels are equal, and also that triangles on the same base and between the same parallels are equal. See Geometry, Props. 35, 37.) * 6. Divide a6 - 3 aV + 3 aV - a? by a? - 3 a?x + 3 oo? -a?. (10.) as...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...parallelogram BD is equal to the parallelogram FH. (Ax. 1.) PROP. XXVIII.— THEOREJL (Euc. I. 37.) Triangles on the same base and between the same parallels are equal in area. r. D c -v „ Let ABC and ABD be two triangles on the same base AB and between the same parallels,...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...equal to the parallelogram EFGH. [Ax. i.] Therefore, parallelograms, &c. QED PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal. * Let the triangles ABC, DBC be on the same ' • base BC, and between the same parallels AD, BC: the...
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The Madras University Calendar, Tom 1

University of Madras - 1876
...side BC is produced to D. Prove that the exterior angle ACD is greater than the angle ABC. III. Prove that triangles on the same base and between the same parallels are equal to one another. (a) Two equal triangles have two sides of the one equal to two sides of the other....
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Chambers's information for the people, ed. by W. and R. Chambers, Tomy 1-2

Chambers W. and R., ltd, Popular educator - 1874
...DE, н к, and they are what we may term symmetrical triangles. From this we learn that symmetrical triangles on the same base and between the same parallels are equal to one another ; and this is true, not for symmetrical Fig. 32. triangles only, but for any triangles,...
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Inventional Geometry: A Series of Problems, Intended to Familiarize the ...

William George Spencer - 1877 - Liczba stron: 97
...322. Take an inch to represent a foot, and make a scale of feet and inches. 323. From the theorem, that triangles on the same base, and between the same parallels^ are equal in surface, can you change a trapezium into a triangle ? 324-. Can you change a triangle into a rectangle...
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The Madras University Calendar, Tom 1

University of Madras - 1879
...coefficient of a,u in the expansion of 1/"(\ + x)3 7.9.11.23 ' -TT - w in ascending powers of x is R / A VII. Triangles on the same base and between the same parallels are equal to one another. ABCD is a quadrilateral figure whose diagonals intersect in E. AD BC are produced to...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...ABCD = /— 7 EFGH. (ax. i) Therefore, parallelograms on equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles on the same base, and between the same parallels, are equal to one another. Let the As ABC, DEC be on the same base BC, and between the same ||s AD, BC. Then shall...
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Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclid, F. B. Harvey - 1880 - Liczba stron: 119
...= the parallelogram EFGH. Wherefore, Parallelograms on equal bases, &c. QED PROP. XXXVII. THEOREM. Triangles on the same base and between the same parallels are equal to one another. Let ABC and DBC be triangles on the same base BC, and between the same parallels AD...
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The student's guide to the University of Durham, with information respecting ...

1880 - Liczba stron: 144
...which join the extremities of equal and parallel straight lines are themselves equal and parallel. 4. Triangles on the same base and between the same parallels are equal. The lines joining the middle points of the sides of a triangle with the opposite angular points meet...
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