 | Edinburgh univ - 1868 - 334 pages
...sides be equal, each to each ; and also the third angle of the one to the third angle of the other. 3. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 4. To divide a given straight line into two parts, so that the rectangle contained by the whole, and... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...Parallelograms which have two sides and the included angle equal in each, are themselves equal. 22. Equivalent triangles upon the same base, and upon the same side of it, are between the same parallels. 23. If the middle points of the sides of a trapezoid, which are not parallel, be joined by a straight... | |
 | Euclides - 1871 - 136 pages
...are taken such that BD = AE. Shew that the triangles CBD, ABE are equal. PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. a Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then must... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...base and on the same side of it are between the same parallels. Corollary 3. — Equal parallelograms upon the same base and upon the same side of it are between the same parallels. DEFINITIONS. 49. — If a rectangle be constructed having its adjacent sides respectively equal to... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...Z>, Enre taken such that BD = AE. Shew that 'riangles CBD, ABE are equal. PROPOSITION XXXIX. THEOREM. Equal triangles upon the same base, and upon the same...it, are between the same parallels. Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then trntst AD be II to BC.... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...parallel to the base upon which they stand.* * This proposition is generally stated thus: — "Equal As upon the same base, and upon the same side of it, are between the same parallels." The meaning of this is just what is stated above, but is less obvious to the beginner. For the construction... | |
 | Euclides - 1874 - 342 pages
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION 39. — Theorem. Equal triangles upon the same base and upon the same...upon the same base BC, and upon, the same side of it. Then the triangles ABC, DBC shall be between the same parallels. Construction. Join AD ; then AD shall... | |
 | Euclides - 1874 - 120 pages
...between ike same parallels. * Let the equal triangles ABC, DBC be on the I • same base BC, and on the same side of it : they shall be between the same parallels. Q Join AD. AD shall be AK-- — 7\D «• parallel to BC. For if it is not, through A draw AE parallel... | |
 | Edward Atkins - 1874 - 428 pages
...it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and on the same side of it ; They shall be between the same parallels. CONSTRUCTION. — Join AD ; AD shall be parallel to BC. - For if it is not, through A draw AE v°se-... | |
 | Edward Atkins - 1876 - 130 pages
...Therefore, triangles, &c. QED Proposition 39. — Theorem. Equal triangles upon the same base, and on the same side of it, are between the same parallels....equal triangles ABC, DBC be upon the same base BC, and on the same side of it ; They shall be between the same parallels. CONSTRUCTION. — Join AD ; AD shall... | |
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EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. 
