| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| 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... | |
| |