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Books Books 1 - 10 of 116 on Therefore, upon the same base, and on the same side of it, there cannot be two triangles....  
" 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 ... - Page 14
by John Playfair - 1806 - 311 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1810 - 518 pages
...if two angles, &c. QED CoR. 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 see which are terminated in one extremity of the base equal to one another, and likewise those which...
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An easy introduction to the mathematics: in which the theory and ..., Volume 2

Charles Butler - Mathematics - 1814
..." 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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 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 - Mathematics, Greek - 1821 - 516 pages
...(ol)tothe angle BDC; but BCD has been proved to be greater than the. same BCD; 'which is impossible. The case in which the vertex of one triangle is upon...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...
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The Elements of geometry [Euclid book 1-3] in general terms, with ..., Part 3

Euclides - 1821
...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 - Geometry - 1822 - 494 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 - 372 pages
...(3.1.) to 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 a side of the other, needs uo demonstration. Therefore, upon the same base, and on the same side of it, there cannot be two triangles,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1826 - 320 pages
...BCD; bnt BDC. has been proved to be greater than the same BCD; whieh is impossible. The ease in whieh the vertex of one triangle is upon a side of the other,...Therefore, upon the same base, and on the same side of it, thereeasnot be two triangles that have their sides whieh are terminated in one extremity of the base...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...two angles, &c. QED COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there can- See N. not be two triangles that have their sides which are terminated in one extremity of the...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...CA, AB are all equal to one another. PROPOSITION VII. THEOREM. Upon the same given straight line and on the same side of it, there cannot be two triangles...their sides which are terminated in one extremity of it equal to one another, and also those which are terminated in the other See Note. extremity. For...
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