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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. "
Euclid's plane geometry, practically applied; book i, with explanatory notes ... - Side 22
av Euclides - 1863
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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volum 2

1844
...upon the same base, and on the same side of it, there cannot be two triangles which have the sides terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity equal. 2. Upon a given straight lino, to describe a segment...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles...the base, equal to one another, and likewise those which are terminated in the other extremity. If it be possible, on the same base AB, and upon the same...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...different situation as EG, FG, then upon the same base EF, and upon the same side of it, 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: but this is impossiblef; therefore, * 7. i. if the base...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...FG ; then, upon the same base EF, and upon the same side of it, there would be two triangles having 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 (I. 7) this is impossible: therefore, if the base...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 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 - 330 sider
...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 extremity, equal to one another." Comprehensive Triangles. The surface...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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
...if, when two 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...the base, equal to one another, and likewise those which are terminated in the other extremity. PART. ENUN. — Let the two AS ACB, ADB be upon the same...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...Hence every equiangular triangle is also equilateral. PROP. VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles...the base, equal to one another, and likewise those which are terminated in the other extremity. PROP. VIII. THEOREM. If two triangles have two sides of...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 sider
...different situation as EG, FG; then, upon the same base EF, and upon the same side of it, 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: But this is impossible (i. 7.) ; therefore, if the base...
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