| GEORGE BRUCE HALSTED - 1885
...CONCLUSION. AB + AC<A'B + AC. PROOF. AA || BC. (253. INVERSE. Equivalent triangles on the same base, **and on the same side of it, are between the same parallels.)** Draw CND _L AA \ meeting BA produced in D. Join A'D. 4NAC = 4ACB, (168. If a transversal cuts two parallels,... | |
| Euclides - 1885
...is equal to half the trapezium. PEOP. XXXIX.— THEOREM. Equal triangles (BAC, BDC) on the same Iase **(BC) and on the same side of it are between the same** parallek. Dem. — Join AD. Then if AD be not parallel to BC> let AE be parallel to it, and let it... | |
| George Bruce Halsted - Geometry - 1886 - 366 pages
...CONCLUSION. AB + AC < A'B + A'C. PROOF. A A' || BC. (253. INVERSE. Equivalent triangles on the same base, **and on the same side of it, are between the same parallels.)** Draw CND ± A A', meeting BA produced in D. Join A'D. 4NAC = £ACB, (168. If a transversal cuts two... | |
| Law - 1889
...point draw a right line parallel to a given right line. 4. Prove that equal triangles on the same base **and on the same side of it are between the same parallels.** 5. The sum of the four angles of any quadrilateral is equal to four right angles. 6. Prove that the... | |
| W. H. Laverty - Dynamics - 1889 - 224 pages
...distances of 9 of the points of division. 40. ABC, DBC are two uniform isosceles triangular laminae **on the same base BC and on the same side of it.** If the centre of mass of the four-sided figure A BDC is at D ; find the ratio of the areas of the two... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...the same base and on the same side of it are between the same parallels. Let ABC and DBC be equal As **on the same base BC, and on the same side of it,** they shall be between the same parallels. Join AD. AD shall be || to BC. For if it is not, through... | |
| Euclid - Geometry - 1890 - 400 pages
.../. A ABP = A CDQ. Proposition 39. THEOREM — Triangles of equal area, which are on the same base, **and on the same side of it, are between the same parallels.** Let AS PAB, QAB be equal in area, and on the same side of same base AB. Assume that the || to AB, through... | |
| Rupert Deakin - Euclid's Elements - 1891 - 79 pages
...can be drawn to a given straight line from a given point without it. 2. BAC and BDC are two triangles **on the same base BC and on the same side of it,** and the angle BAG is equal to the angle BDC. Prove that each of the vertices A and D must lie without... | |
| Queensland. Department of Public Instruction - Education - 1892
...three given lines is not less that the sum of the other two. 20 5. Equal triangles on the same base **and on the same side of it are between the same parallels.** 22 G. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles... | |
| Euclid - Geometry - 1892 - 518 pages
...and mi the xnnic side of it, ar?, between the same parallels. Let the triangles ABC, DBC which stand **on the same base BC, and on the same side of it,** be equal in area : then shall they be between the same parallels ; that is, if AD be joined, AD shall... | |
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