| Samuel H. Winter - 1877 - 452 pages
...be greater than the third. How would the process fail if the last condition were not fulfilled ? 2. **Parallelograms on the same base and between the same parallels are equal** to each other. Show that if two triangles have two sides of the one equal to two sides of the other,... | |
| James Maurice Wilson - 1878 - 450 pages
...difference of identically equal magnitudes are equal, although they may not be identically equal. THEOREM i. **Parallelograms on the same base and between the same parallels are equal.** Part. En. Let ABCD, EBCF\iz parallelograms, upon the same base BC, and between the same parallels AF,... | |
| Rolla Rouse - 1879 - 400 pages
...is unscientific, as it 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... | |
| University of Oxford - Greek language - 1879 - 414 pages
...and ratio. 7. Triangles 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... | |
| Euclides - 1879 - 146 pages
...opposite sides to two 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.... | |
| W J. Dickinson - Geometry - 1879 - 44 pages
...parallelogram will be divided into four equal parts ; in what case will the diagonal bisect the angle ? 35. **Parallelograms on the same base and between the same parallels are equal** to one another. What is the converse of this proposition ? Same proposition. Describe a parallelogram... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...parallelogram ACDB into two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. **Parallelograms on the same base, and between the same parallels, are equal** to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels... | |
| T S. Taylor - 1880 - 152 pages
...parallelogram. The enunciations of Euc. I. 4, I. 29, and I. 34. And Axioms 2a, 30, and 6. General Enunciation. **Parallelograms on the same base, and between the same parallels, are equal** to one another. Particular Enunciation (CASK I). Given — The parallelograms ABCD, DBCF, on the same... | |
| Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...diagonals, intersecting in E ; prove that AE and BE = CE and DE, each to each. PROP. XXXV. THEOREM. **Parallelograms on the same base, and between the same parallels, are equal** to each other. Let ABCD and EBCF be parallelograms on the same base BC, and between the same parallels... | |
| 1880 - 160 pages
...angles ; and the three interior angles of every triangle are together equal to two right angles. (v.) **Parallelograms on the same base, and between the same parallels, are equal** to one another. (vi.) In any right angled triangle, the square which is described on the side subtending... | |
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