| W J. Dickinson - Geometry - 1879 - 44 pages
...angle. 36. Parallelograms upon equal bases and between the same parallels are equal to one another. 37. **Triangles upon the same base and between the same parallels are equal to one another.** Any point P is taken in the line joining an angular point A of a triangle to the middle point of the... | |
| Great Britain. Parliament. House of Commons - Great Britain - 1879 - 632 pages
...possible ? Show how the construction will fail if the condition is not observed. 4. Parallelograms **upon the same base and between the same parallels are equal to one another.** 5. In any right-angled triangle the square which is described upon the side subtending the right angle... | |
| Euclides - 1879 - 146 pages
...opposite angles : these lines trisect the given line. PROPOSITION XXXV. THEOREM. Parallelograms on the **same base, and between the same parallels, are equal to one another. Let the** / — 7s ABCD, EBCF be on the same base BC, and between the same ||s AF, BC. Then shall /— 7 ABCD... | |
| 1879 - 636 pages
...possible ? Show how the construction will fail if the condition is not observed. 4. Parallelograms **upon the same base and between the same parallels are equal to one another.** 5. In any right-angled triangle the square which is described upon the side subtending the right angle... | |
| Joseph Wollman - 1879 - 120 pages
...is parallel to SR (I. 30). Similarly it can be proved that LO is parallel to PS. QED SECTION III. 1. **Triangles upon the same base and between the same parallels are equal.** Construct a triangle equal to a given triangle and having a base three times as great. Let LMN xbe... | |
| Rolla Rouse - 1879 - 402 pages
...gives four propositions where only one is required. Proposition 35, stating that parallelograms on the **same base and between the same parallels are equal to one another** ; Proposition 36, that on equal bases and between the same parallels they are equal ; and 37 and 38,... | |
| University of Oxford - Greek language - 1879 - 412 pages
...and parallelograms of the same altitude are to one another as their bases. 8. Parallelograms on the **same base, and between the same parallels, are equal to one another.** 9. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
| William Stanley Jevons - Economics - 1879 - 430 pages
...investment of the whole amount. In the 37th proposition of the first book of Euclid it is proved that all **triangles upon the same base and between the same parallels are equal** in area. Hence we may draw the conclusion that, provided capital be invested and uninvested continuously... | |
| Edward Harri Mathews - 1879 - 94 pages
...equal to two right angles. What ratio does the angle of a regular hexagon bear to a right angle ? 2. **Triangles upon the same base and between the same parallels are equal.** A line drawn through the middle points of the sides of a triangle is parallel to the base. 3. In any... | |
| University of Madras - 1879 - 674 pages
...expansion of 1/"(\ + x)3 7.9.11.23 ' -TT - w in ascending powers of x is R / A VII. Triangles on the **same base and between the same parallels are equal to one another.** ABCD is a quadrilateral figure whose diagonals intersect in E. AD BC are produced to meet at O. OP... | |
| |