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" 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 extremity. "
The first three books of Euclid's Elements of geometry, with theorems and ... - Side 11
av Euclid, Thomas Tate - 1849 - 108 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 sider
...FG ; then, upon the same base EF, and upon the same side of it, there can he two triangles EDF, EGF, that have their sides which are terminated in one...extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7. 1.) ; therefore, if the...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - 1846 - 368 sider
...evident from the theorem, (Euclid, 7, I.) which proves that, "Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated in the other...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 sider
...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 also those terminated in the other extremity. If it be possible, let there be two triangles ACB, ADB,...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 sider
...sides of a A &c. — Q, ED PROP. VII. THEOR. GEN. ENUN. — Upon the same base, and on the same side of it, there cannot be two triangles that have their...those which are terminated in the other extremity. PART. ENUN. — Let the two AS ACB, ADB be upon the same base AB, and the same side of it, and let...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1847 - 340 sider
...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...which are terminated in one extremity of the base equai to one another, and likewise those which are terminated in the other extremity, equal to one...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 sider
...equiangular triangle is also equilateral. PROP. VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles that have their...those which are terminated in the other extremity. PROP. VIII. THEOREM. If two triangles have two sides of the one equal to two sides of the other, each...
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Papers for the Schoolmaster, Volum 2

1852 - 316 sider
...Taylor. EUCLID. DIVISION I. SECTION I. 1. Upon the same base and upon the same side of it there canuot be two triangles that have their sides which are terminated...one another, and likewise those which are terminated at the other extremity. 2. The greater side of every triangle is opposite the greater angle. 3. To...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - 1851 - 826 sider
...evident from the Theorem (Euclid 7. 1.) which proves that " Upon the same base, and on the same side of it, there cannot be two triangles that have their sides, which are terminated at one extremity of the base, equal to one another, and likewise those which are terminated in the...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 sider
...different situation as EG, FG; then, upon the same base EF, and upon the same side of it, BOOK I. there can be two triangles that have their sides which are terminated...extremity of the base equal to one another, and likewise their sides terminated in the other extremity: • vii. i. But this is impossible"; therefore, if the...
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Five Years in an English University, Volum 2

Charles Astor Bristed - 1852 - 470 sider
...those only who send in no answers to the lastj paper.) 1. UPON the same base, and on the same side of it, there cannot be two triangles that have their...are terminated in one extremity of the base equal to each other, and likewise those which are terminated in the other. 2. If the sides of a triangle be...
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