 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...and D, show that two sides of the quadrilateral are parallel to each other. (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.... | |
 | College of preceptors - 1882 - 528 pages
...Having proved this proposition, state the two corollaries, but^rwe only one of them. 7- Equal triangles on the same bas,e, and on the same side of it, are between the same parallels. 8. To a given straight line to apply a parallelogram that shall be equal to a given triangle, and have... | |
 | 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... | |
 | 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 ||... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...parallel to the base ; this is shewn in I. 37 and I. 39. Again, the locus of the vertices of all triangles which are on the same base and on the same side of it, and which have the same vertical angle, is a segment of a circle described on the base ; for it is... | |
 | William James Browne - Mechanics - 1883 - 218 pages
...(or thin plate) is said to be of uniform density ? (10.) 2. If a number of equal triangular laminae are on the same base and on the same side of it, their centres of gravity will be in the same straight line. Why is this, and where is the line situated... | |
 | 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... | |
 | 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 - 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,... | |
 | 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... | |
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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. 
