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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Inventional Geometry: A Series of Problems, Intended to Familiarize the ... - Página 43
por William George Spencer - 1877 - 97 páginas
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...points. P. 31. Through a given point to draw a st. line parallel to a given st. line. DEM. — P. 37. Triangles upon the same base and between the same parallels are equal. Ax. 1. Magnitudes equal to the same magnitude are equal. EXP. 1 HypConcl. Let the AS ABC, DEC, A be...
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Elements of geometry, containing the first two (third and fourth ..., Parte1

Euclides - 1871
...[3EBCH= EJEFGH, i. 35. V they are on the same base EH and between the same IIs ; .-. O ABCD =o EFGH. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same lis AD. BC. Then must &ABC= &DBC. From B draw...
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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 páginas
...proved equal to the area of AF, therefore the area of AF is equal to the area of GD. PROPOSITION 6. Triangles upon the same base and between the same parallels are equal to one another in area. Fig. 14. j) AD P Let the triangles ABC and DBC be upon the same base BC, and between the same...
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Key to the Irish commissioners' Treatise on mensuration

William Kennedy Maxwell - 1871
...ft. 13. Here, as 4-1 : 65 : : 5 : 79-26, the height of the pole. Ans. 14. Now, triangles that stand upon the same base, and between the same parallels are equal to each other ; therefore, this question will, as shown in the figure, admit of two answers. Here, the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 páginas
...CJEFGH, i. 35. v they are on the same base EH and between the same IIs ; QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same IIs AD, BC. Then must &ABC= A DBC. From B draw...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - 1872
...ABCD and EFGH, being each equal to the parallelogram ABGH, Are equal to each other. PBOPOSITION XXXVU. Triangles upon the same base and between the same parallels are equal to each other. For the construction in this proposition we must be ableto draw a straight line from a...
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First book of mathematics

Hugo Reid - 1872 - 124 páginas
...produced. 142. If ote. — This illustrates the important geometrical truth, that — Parallelograms on the same base and between the same parallels are equal to one another; that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the same parallels...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...decimals. (10.) 21 41 21 228 2000 _1824 1~7G, <fcc. (See Arith., § 61.) * 3. Show that parallelograms and triangles upon the same base and between the same parallels are equal to one another. (10.) (This appears to mean that parallelograms on the same base and between the same parallels are...
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Pure mathematics, Volumen1

Edward Atkins - 1874
...Therefore the parallelogram ABCD is equal to the parallelogram EFGH (Ax. 1). Proposition 37. — Theorem. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be on the same base BC, and between the same parallels AD, BC ; The triangle...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...divides the parallelogram ACDB into two equal parts. ~ QED PROPOSITION 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC....
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