 | Isaac Todhunter - 1880 - 426 σελίδες
...[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. QEI). PROPOSITION 3. THEOREM.... | |
 | James Russell Soley - 1880 - 346 σελίδες
...straight lines is invariable. Under what conditions will this difference be zero ''. 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The sides AB and AC of a triangle are bisected in D and K respectively, and SE, CD are produced until... | |
 | Euclides, Frederick Burn Harvey - 1880 - 178 σελίδες
...triangle DEF. Wherefore, Triangles on equal bases, 'Ssc. QED PROP. XXXIX. THEOREM. Equal triangles on the same base, and on the same side of it are between the same parallels. Let ABC and DBC be equal triangles, on the same base BC and on the same (viz. the upper) side of it.... | |
 | John Gibson - 1881 - 64 σελίδες
...another. 3. Triangles on the same base and between the same parallels are equal. 4. Equal triangles on the same base and on the same side of it are between the same parallels. 5. Prove that the diagonals of a parallelogram bisect each other. 6. Bisect a given triangle by a straight... | |
 | George Bruce Halsted - 1881 - 258 σελίδες
...intercepted spherical triangle, is constant. MENSUBATION. 345. Equivalent spherical triangles upon the same base, and on the same side of it, are between the same parallel and equal lesser circles of the sphere. 346. The locus of JB, the vertex of a spherical triangle... | |
 | 1881 - 504 σελίδες
...right angles as the figure has sides. 5. Equal triangles upon equal bases in the same straight line, and on the same side of it, are between the same parallels. The straight line joining the points of bisection of two sides of a triangle, is parallel to the base.... | |
 | Marianne Nops - 1882 - 278 σελίδες
...the reference to I. 3S instead of I. 37. SUMMART OF PROPOSITION XXXIX., THEOBEM 29. Equal triangles on the same base and on the same side of it are between the same parallels. Cons.—Dr&w AE || to BC. Join EC. Proof (Indirect).— A ABC = A EBC (I. 37). A ABC = A DBC (Hyp.).... | |
 | College of preceptors - 1882 - 528 σελίδες
...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... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 σελίδες
...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.... | |
 | Euclides - 1883 - 176 σελίδες
...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 ||... | |
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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. 
