| Thomas Fowler - 1887 - 365 sider
...which our deductive reasoning proceeds. The proposition proved in Euclid, Book i. Prop. 38, that ' **Triangles upon equal bases, and between the same parallels, are equal to one another,'** is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon... | |
| Canada. Department of the Interior - 1888
...sides of the other, each to each, the triangles shall be eqnal in all respects. 2. Parallelograms on **equal bases and between the same parallels are equal to one another.** 3. If a straight line be divided into two equal, and also into two unequal parts, the squares on the... | |
| E. J. Brooksmith - 1889
...angles. No straight line can be placed within a parallelogram greater than the greater diameter. 3. **Triangles upon equal bases, and between the same parallels, are equal to one another.** The line AD is drawn from the vertex of the isosceles triangle ABC perpendicular to the base, and is... | |
| John Fry Heather - 1890 - 172 sider
...EQUIVALENT AND SIMILAR FIGURES. THEOREMS. 214. THEOR. 29. — Parallelograms and triangles upon the same or **upon equal bases, and between the same parallels, are equal to one another.** (Eu. I. 35 — 38.) 215. THEOR. 30. — If a parallelogram and a triangle be upon the same base and... | |
| Royal Institute of British Architects - 1890
...rectilineal angle, ie, to divide it into two equal parts. (Euclid, Bk. 1, prop. 9). 11. Parallelograms **upon equal bases and between the same parallels are equal to one another.** (Euclid, Bk. 1, prop. 36).* Tuesday Afternoon: one hour and a half. GEOGEAPHY AND HISTORY. Hon. Examiner:... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...DBC is half of the ||gm DBCF, [I. 34. ... A ABC = ADBC. [Ax. 7. PROPOSITION 38. THEOREM. Triangles on **equal bases and between the same parallels are equal to one another.** Let ABC and DEF be As on equal bases, BC and EF, and between the same parallels BF and AD, then ABC... | |
| Euclid - 1890 - 400 sider
...equal in area. Now A ABP = half a ABPX, and A ABQ = half a ABYQ ; /. A ABP = A ABQ. Proposition 38. **THEOREM — Triangles upon equal bases, and between the same parallels, are equal** in area. Let A» PAB, QCD be on equal bases AB, CD, and between the same ||" PQ, AD. Draw AX || to... | |
| Rupert Deakin - 1891 - 79 sider
...Triangles on the same base and between the same parallels are equal to one another. 38. Triangles on **equal bases and between the same parallels are equal to one another.** 39. Equal triangles on the same base and on the same side of it are between the same parallels. 40.... | |
| 1893
...dates are chiefly produced, and where gold, coal, and tin are found. EUCLID (BOOKS I.-IV. )— (i) **Triangles upon equal bases and between the same parallels are equal to one another.** The base BC of the triangle ABC is bisected in D, and through B a line is drawn meeting AC in E and... | |
| 1894
...EBCF be two parallelograms. Then ABCD is equal in area to EBCF. IX. Triangles upon the same base, or **upon equal bases, and between the same parallels are equal to one another.** Thus the triangle ABC, Fig. 25, is equal in area to the triangle DEF. X. A triangle is equivalent to... | |
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