 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 páginas
...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.... | |
 | Marianne Nops - 1882 - 278 páginas
...method. They show that equal triangles on the same base, and on equal bases in the same straight line, and on the same side of it, are between the same parallels. Let us take equal triangles ABC, DBC on the same base EC. Joining the vertices of the triangles, we... | |
 | College of preceptors - 1882 - 528 páginas
...proposition in the course of the proof of which reference is made to it. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. Prove that diameters (produced, if necessary) of any pair of parallelograms about the diameter of a... | |
 | 1886 - 568 páginas
...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 - 1883 - 428 páginas
...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 páginas
...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 - 182 páginas
...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.... | |
 | 1884 - 708 páginas
...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 páginas
...triangles &c. QED PROPOSITION XL. THEOREM. Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels. GIVEN that the triangles ABC and DEF are equal, and on the equal bases BC, EF, which are in the same... | |
 | Euclides - 1884 - 434 páginas
...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... | |
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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. 
