 | 582 pages
...3i per cents, at 97, and what change in income rould be thus effected ? EUCLID. « SECTION I. '• Upon the same base and on the same side of it, there cannot be two "angles, which have their sides which arc terminated in one extremity of the 'ase cqual to one another,... | |
 | Euclides - 1852 - 152 pages
...equal to DA, or CB equal to DB. It is not possible that both CA can be equal to DA, and CB equal to DB. The case in which the vertex of one triangle is upon a side of the other, is shown in the annexed figure; where it is manifest that, whether CA be equal to DA or not, CB cannot... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...angle BCD ; but BDC has been proved to be greater than the same BCD ;. which is impossible. TheHcaso in which the vertex of one triangle is upon a side...that have their sides which are terminated in one extrem ity of the base equal to one another, and likewise those which are termina ted in the other... | |
 | Euclides - 1853 - 146 pages
...equal to the angle 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...Therefore, upon the same base, and on the same side of it, &c. QED PROP. VIII. — THEOREM. . If two triangles have two sides of the one equal to two sides of... | |
 | Euclides - Geometry - 1853 - 176 pages
...angle b С d ; but bd С has been proved to be greater than the same b С d ; which is impossible. The case in which the vertex of one triangle is upon...Therefore, upon the same base, and on the same side of it, &c. QED PROPOSITION VIII. — THEOREM. If two triangles have two sides of the one equal to two sides... | |
 | Euclides - Geometry - 1853 - 334 pages
...all equal, that is, the triangle ABC is equilateral (Def. 24). Which was to be proved. PEOP. VII. On the same base and on the same side of it there cannot be two triangles which have their sides terminated in one extremity of the base equal, and likewise those terminated... | |
 | Euclides - 1855 - 270 pages
...Therefore, the angle BDC is both equal to, and greater than the angle BCD, which is impossible. The third case, in which the vertex of one triangle is upon...the other needs no demonstration. Therefore, upon th« same base, and on the same side of it, &c. QED The third case needs no demonstration, because... | |
 | John Playfair - Geometry - 1855 - 334 pages
...is, it is equal to it. Coa. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there cannot be two triangles, that have their sides whieh are terminated in one extremity of the base equal to one another, and likewise those which are... | |
 | Cambridge univ, exam. papers - 1856 - 200 pages
...left, so as not to topple over. EUCLID. BOOKS I. II. Ill (A). For all Candidates for a BA Degree. 1. UPON the same base and on the same side of it, there cannot be two triangles, which have their sides terminated in one extremity of the base equal to one another and likewise those... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...'86. Approximate as far as 4 places of decimals to the square roots of 7, i, and If. Euclid. 1. On the same base, and on the same side of it, there cannot be two triangles that have the sides terminated in one extremity of the base equal to one another, and likewise those terminated... | |
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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... 
