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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 44
by Nathan Scholfield - 1845
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...preceding books. 1. Thus it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area : and hence, if only the base and area of a triangle be given, its vertex may be at any point...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...sections of their cylinders ; viz.. the ungulical section FC has the same relation to the cylindric section FA. as the ungulical section IL has to the...which it is erected, or less than that base. Cor. 1. As the same arguments would apply to conical ungulas.it may be inferred that conical ungulas of...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...sections of their cylinders ; viz., the ungulical section FC has the same relation to the cylindric section FA, as the ungulical section IL has to the...which it is erected, or less than that base. Cor. 1. As the same arguments would apply to conical ungulas, it may be inferred that conical ungulas of...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...preceding books. 1. Thus, it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area: and hence, if only the base and area of a triangle be given, its vertex may be at any point in...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...that BQ is equal to QP and OP to PQ. M E PROP. XXVI.— THEOREM. (Euc. I. 35.) Parallelograms standing on the same base, and between the same parallels, are equal in area. Let ABCD bo a parallelogram on the base AB; it is required to prove that - it is equal in area...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - Circle - 1875 - 172 pages
...which are the complementary parallelograms, are (Ax. 3) equal in area, as stated. 6. Parallelograms on the Same Base and between the Same Parallels are equal in area. Bl Ot Let AB be the common base, and ABA.B, and ABA B2 two such parallelograms on AB and between...
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Inventional Geometry: A Series of Problems, Intended to Familiarize the ...

William George Spencer - Geometry - 1877 - 108 pages
...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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A Popular History of Science

Robert Routledge - Electronic books - 1881 - 748 pages
...the reasoning can easily be followed by any one conversant with tht geometrical fact that triangks on the same base and between the same parallels are equal in area. Let a body be moving unacted on by any F force along the line AD, Fig. 85 ; in that line its...
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Inventional Geometry: A Series of Problems, Intended to Familiarize the ...

William George Spencer - Geometry - 1881 - 116 pages
...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 trapezi um into a triangle ? 324. Can you change a triangle into a rectangle...
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The papers set at the professional preliminary examination

College of preceptors - 1882
...two sides of a triangle and the third side. 3. Define a parallelogram ; and show that parallelograms on the same base and between the same parallels are equal in area. Enunciate a converse of this proposition. 4. Define an acute-angled triangle, an obtuse-angled...
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