 | Euclid, James Thomson - 1837 - 410 pàgines
...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 - 1845 - 894 pàgines
...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... | |
 | Nathan Scholfield - 1845 - 506 pàgines
...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... | |
 | Euclid, James Thomson - 1845 - 382 pàgines
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pàgines
...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 - 1875 - 196 pàgines
...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 - 1877 - 108 pàgines
...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 - 1881 - 748 pàgines
...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 - 1881 - 116 pàgines
...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... | |
 | College of preceptors - 1882 - 528 pàgines
...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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Prove that parallelograms on the same base and between the same parallels are equal in area. 
