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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... "
Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 12
by Euclides - 1842
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...the triangle possesses this property is 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...equal to that of the triangle (4. 1.) ACB, the less to the greater ; which is absurd. Therefore, AB is not unequal to AC, that is, it is equal to it. COR. Hence every equiangular triangle is also equilateral. PR0B. VII. THEOR. •» Upon the same base,...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 pages
...subtraction, AB = AC. Wherefore, 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 that have their sides, which are terminated in one extremity of the base, equal to one another, and...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...equal to one another. COR. 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 that have their sides which are terminated in one extremity of the base, equal to one another, and...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...triangle DBC is equal to the triangle (i. 4.) ACB, the less to the greater; which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it....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...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...triangle DBC is equal to the triangle ACB (Prop. VI.), the less to the greater, which is absurd. Hence AB is not unequal to AC, that is, it is equal to it. Therefore, if two angles, &c. Cor. Hence, every equiangular triangle is also equilateral. PROPOSITION...
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Minutes of the Committee of Council on Education, Volume 1

Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...rule for determining the surface of a sphere. GEOMETRY. Section 1 . 1. Upon the same base, and upon the same side of it, there cannot be two triangles having their two sides terminated at one extremity of the base equal, and likewise their two sides terminated at...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...the triangle possesses this property is 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...
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Papers for the schoolmaster, Volumes 1-6

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

Euclides - 1852 - 152 pages
...triangle DBC is equal to the triangle b ACB, the less to the greater; which is absurd. Therefore AB is not unequal to AC ; that is, it is equal to it. Wherefore, if two angles, &c. QED COK. Hence every equiangular triangle is also equilateral. [To exhibit the truth of this, draw first...
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