 | 1886 - 568 pages
...two sides of a triangle are together greater than the third side. 4. Equal triangles on the same base and on the same side of it, are between the same parallels. 5. If a straight line be divided into two equal, and also into two unequal parts, the squares on the... | |
 | Euclides - 1883 - 176 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 - 708 pages
...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 - 214 pages
...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 - 182 pages
...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 - 434 pages
...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 - 322 pages
...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 - 340 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 - 1304 pages
...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 - 358 pages
...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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Equal triangles on the same base, and on the same side of it, are between the same parallels. 
