 | 1886 - 568 pages
...theorem. 8. Any 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...[V. 9. And these triangles are on the same base DE and on the same side of it ; but equal triangles on the same base, and on the same side of it, are between the same parallels ; [I. 39. therefore DE is parallel to BC. "Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM.... | |
 | Euclides - 1883 - 176 pages
...34), and A DEF is 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 ||... | |
 | Euclides - 1884 - 214 pages
...Axiom 7. Therefore, triangles on equal bases &c. QED po 10 PROPOSITION XXXIX. THEOREM. Equal triangles on the same base, and on the 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,... | |
 | Euclides - 1884 - 182 pages
...and D, show that 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
...side opposite. 1. 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... | |
 | Education - 1884 - 708 pages
...isosceles that is 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... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...straight lines is 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... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...having the same base. 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,... | |
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DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 
