 | Euclides - 1883 - 176 pages
...(proved), .-. L ACB = L ABC (Ax. 3), and these are the angles at the lose. QED EU. I. 7. THEOR. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise... | |
 | Euclides - 1884 - 94 pages
..., wherefore the angle is both equal to, and greater than the angle ; which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base and on the same side of it, &c. RELFE BROTHERS' EUCLID SHEETS, PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM... | |
 | Stewart W. and co - 1884 - 272 pages
...BDC is equal to BCD ; but BDC has been proved to be greater than the same BCD, which is impossible. The case in which the vertex of one triangle is upon a side of the other, needs no demonstration. VIII. — If two triangles have two sides of the one equal to two sides of the other, each to each,... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1884 - 154 pages
...line joining the point of section to the vertex, is equal to the square on one of the equal sides. 5. Upon the same base, and on the same side of it, there cannot be two triangles having their sides terminated in one extremity of the base, equal to one another, and likewise those... | |
 | Palaestra Oxoniensis - 1884 - 204 pages
...following enunciations : — (i) Describe an equilateral triangle upon a given finite straight line. (2) Upon the same base and on the same side of it there cannot be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
 | Henry William Watson - 1884 - 320 pages
...greater than AB + CD. But AE+CE is equal to AC, and EB + ED is equal to DB, '|L~ 7 PROPOSITION 4. £5to# the same base and on the same side of it there cannot be two triangles having the two sides terminated in one extremity of the base equal to each other, and at the same time... | |
 | Euclides - 1884 - 214 pages
...angle BA C is equal to the angle EDF. Axiom 8. Therefore if two triangles dtc. QED Proposition VII. On the same base and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise... | |
 | 1884 - 266 pages
...VI., with the Definitions of Book V.) (Optional.) Time allowed, 2 hours.—(Including Reading.)* 1. Upon the same base and on the same side of it, there cannot be two * A passage (not printed here), occupying about 20 lines of an ordinary reading book, was set in this... | |
 | Euclides - 1884 - 182 pages
...pair. (Join A,B,C,Dto the centre, and use I. 5 four times.) SECTION II. PROPOSITIONS 7—12. VI. 1 . If upon the same base and on the same side of it there be two triangles, and one of them be equilateral, prove that the other is not equilateral. 2. In equal... | |
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Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal... 
