| Euclides - 1883 - 96 pages
...half Q EH, .-. A ABC = A DEF (Ax. 7). QED HU TYTv PROP. 39. THEOK. Equal triangles on the same base **and on the same side of it are between the same parallels.** Given A ABC = A DBC, on same AD base BC. To prove AD || BC. If AD is not || BC, through A draw AE ||... | |
| Education - 1884
...BA=BE, but BE = AC. Л the triangle ABC is isosceles. Q- b- °2. Equal triangles upon the same base **and on the same side of it are between the same parallels.** Prop. 39, Bk. I. 3. To a given straight line to apply a parallelogram, which shall be equal to a given... | |
| Euclides - 1884
...same side of it are between the same parallels. GIVEN that the triangles A BC and DBC are equal, and **on the same base BC and on the same side of it,** and that AD is joined ; IT is REQUIRED TO PROVE that AD is parallel to BC, From A draw AE parallel... | |
| Euclides - 1884
...two sides of the quadrilateral are parallel to one another. (10) 10. Equal triangles on the same base **and on the same side of it are between the same parallels.** If a quadrilateral is divided into four equal triangles by its diagonals, show that it is a parallelogram.... | |
| Euclides - 1884
...Prove the proposition for the case when the points D and E coincide. 2. Equal ||m8 on the same base **and on the same side of it are between the same parallels.** 3. If through the vertices of a triangle straight lines be drawn || the opposite sides, and produced... | |
| Euclides - 1885
...DBCF ; and they are equal, since each is double of A DBC. I. 34 2. Let ABCD, EBCF be two equal ||m' **on the same base BC, and on the same side of it.** If AD, or AD produced, be not in the same straight line with EF, let it cut BE and CF, or these straight... | |
| Euclid, John Casey - Euclid's Elements - 1885 - 312 pages
...is equal to half the trapezium. PEOP. XXXIX.— THEOREM. Equal triangles (BAC, BDC) on the same bose **(BC) and on the same side of it are between the same parallels.** Dem. — Join AD. Then if AD be not parallel to BC, let AE be parallel to it, and let it cut BD in... | |
| United States. Congress. Senate - United States - 1880
...invariable. Under what conditions will this difference be /ею :' 2. Equal triangles on the same base, **and on the same side of it, are between the same parallels.** The sides .11! and .K'of a triangle are bisected in I) and E respectively, and RE, CD are produced... | |
| Oxford univ, local exams - 1885
...parallelograms about the diameter of a square are likewise squares. 5. Equal triangles on the same base, **and on the same side of it, are between the same parallels.** 6. If a straight line be bisected, and produced to any point, the square on the whole line thus produced,... | |
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