| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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