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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 36
by Nathan Scholfield - 1845
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 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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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...AB, -and the two ungulas will be equivalent, or equal in solidity. For each section FC or IL of the two ungulas parallel to the base BD, have the same...Cor. 1. As the same arguments would apply to conical ungulas, it may be inferred that conical ungulas of the same base and equal altitude are equivalent,...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...sections of their cylinders ; viz., the ungulical section FC has the •ame relation to the cylindrie section FA, as the ungulical section IL has to the...which it is erected, or less than that base. Cor. I. 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 - 352 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
...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 - Science - 1881 - 673 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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Class lessons on Euclid

Marianne Nops - 1882
...easier. Only one case is given by Euclid. SUMMARY OF PROPOSITION XXXV., THEOREM 25. Parallelograms on the same base and between the same parallels are equal in area. Cons. — Nil. Case I. Each \^m is double of A DEC (I. 34). .-. Hg™™ are equal. Cases II....
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