 | Edward Atkins - 1874 - 428 pages
...the triangle DEF. Therefore, triangles, &c. QED Proposition 39.— Theorem. Equal triangles upon tlie same base, and on the same side of 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...AR, and . -. = square on AQ, which is impossible; PROBLEM (,/). Find the locus of the vertices of all triangles, on the same base and on the same side of it, having a given vertical angle. R Let AB be the given base, and Q the given angle. On AB describe a... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...therefore the triangle BDE is equal to the triangle CDE: (v. 9.) and they are on the same base DE: but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 39.) therefore 1iE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III... | |
 | Edward Atkins - 1876 - 130 pages
...to the triangle DEF. 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. Let the equal triangles ABC, DBC be upon the same base BC, and on the same side of it ; They shall... | |
 | Education Department,London - 1876 - 1010 pages
...base ; find a point P within the triangle, such that the triangles РЛВ, PBC, PCA may be equal. 2. Equal triangles on the same base and on the same side of it are beUveen the same parallels. 3. The square on the sum of two lines is equal to the square on their difference... | |
 | Euclides - 1877 - 58 pages
...— Hence every equilateral triangle is also equiangular. Exercises. 1. ABC, DBC are two isosceles triangles on the same base and on the same side of it ; prove that AD bisects the angle BA C. 2. If two isosceles triangles stand upon opposite sides of... | |
 | Stephen Thomas Hawtrey - 1878 - 202 pages
...the same space; then he has before him exactly the case contemplated in Proposition VII., viz., two triangles on the same base, and on the same side of it, having the two sides ending in one extremity of the base equal to each other, and likewise the two... | |
 | Edward Harri Mathews - 1879 - 94 pages
...prove Euclid's second corollary to this proposition, and state under what limitation it is true. 2. Equal triangles on the same base and on the same side of it are between the same parallels. If a quadrilateral is bisected by each of its two diagonals, it is a parallelogram. 3. In any right... | |
 | Isaac Sharpless - Geometry - 1879 - 282 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... | |
 | Euclides - 1879 - 146 pages
...a side of the other needs no demonstration. Therefore, on the same base, &c. QED [Hypothesis : two triangles on the same base and on the same side of it. Conclusion : they cannot have their sides which are terminated at one extremity of the base equal to... | |
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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. 
