 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...triangle ABC = the 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.... | |
 | T S. Taylor - 1880 - 152 pages
...(Euclid I. 39). Repeat. — The enunciations of Euc. I. 31, I. 37, and Axiom r. 3 General Enunciation. Equal triangles on the same base and on the same side of it are between the same parallels. Particular Enunciation. Given. — The triangles ABC, DBC on the same base BC and on the same side... | |
 | James Russell Soley - Naval education - 1880 - 346 pages
...upon two given 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... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...is equal to three times the arc AE. 230. The straight lines which bisect the vertical angles of all triangles on the same base and on the same side of it, and having equal vertical angles, all intersect at the same point. 231. If two circles touch each other... | |
 | Education, Higher - 1883 - 536 pages
...segments of circles. When is a rectilineal figure said to be inscribed in another rectilineal figure ? 9. Equal triangles on the same base, and on the same side of it are between the same parallels. 10. Describe a square that shall be equal to a given rectilineal figure. 12. One circle cannot touch... | |
 | John Gibson - 1881 - 64 pages
...are equal to one 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 - Measurement - 1881 - 258 pages
...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... | |
 | Education, Higher - 1881 - 504 pages
...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.... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...triangles, of which the triangles will be halves, and apply Prop. 34.) Proposition 37. Theorem. — Equal triangles on the same base and on the same side of it are between the same parallels, Let ABC, DBC be equal triangles on the same base BC; they will be between the same parallels. For if... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...to those at C 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.... | |
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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. 
