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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... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Side 14
av John Playfair - 1806 - 311 sider
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Papers for the schoolmaster, Volumer 1-6

582 sider
...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,...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 sider
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 336 sider
...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...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 sider
...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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 sider
...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...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bok 1

Euclides - 1853 - 334 sider
...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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 sider
...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...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 334 sider
...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...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 sider
...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...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 sider
...'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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