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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. "
Modern geometry [ed.] with an appendix by W.B. Jack - Page 239
by Richard Wormell - 1876
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...in which the vertex of one triangle is upon a side of the other, needs no demonstration. 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...in which the vertex of one triangle is upon a side of the other, needs no demonstration. 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...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...which subtend, or arc. opposite to» the equal angles, shall be equal to one another. Prop. VII. Theor. 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...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
..." for if -4EB do not coincide with CFD, it must fall otherwise (as in the figure to prop. 23.) then upon the same base, and on the same side of it, there will be two similar segments of circles not coinciding with one another, but this has been shewn (in...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...in which the vertex of one triangle is upon a side of the other, needs no demonstration. 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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...two angles, &c. QED II C COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the. same base, and on the same side of it, there caitnot be two triangles, that have their sides which are terminated in one extremity of the base equal...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...triangle is upon a side of the other, needs no demonstration. "** 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...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...every equiangular triangle is equilateral ; vide, Elrington. PROP. 7. THEOR. i On the same right line and on the same side of it there cannot be two triangles formed whose conterminous sides are equal. If it be possible that there can, 1st, let the vertex of...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...it are equal, and therefore the sides opposite to them. PROP. VII. THEOR. Upon the same base (AB), and on the same side of it, there cannot be two triangles (ACB, ADB), whose conterminous sides are equal, (namely AC to AD, and BC to BD). For, if possible,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...&c. QED COR. Hence every equiangular triangle is also equal equilátera. Proposition Vll. 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 likewise those which are...
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