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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: Containing the First Six Books of Euclid, with a ... - Página 9
por John Playfair - 1844 - 317 páginas
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 páginas
...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»; therefore, if the base BC...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 páginas
...FG; then, upon the same base EF, and upon the same side of it, there can be two triangles EDF, EGF, that have their sides which are terminated in one extremity of the base equal to one Book I. another, and likewise their sides terminated in the other \^f>fn^ extremity : but this is impossible*...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 páginas
...Therefore AB is not D unequal to AC, that is, it is equal to it. J — Wherefore, if two angles, &c. QED CoR. Hence every equiangular triangle is also equilateral....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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volumen5

John Mason Good - 1813 - 714 páginas
...the sides also 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...those which are terminated in the other extremity. Prop. VIII. Theor. If two triangles have two sides of the one equal to two sidfs of the other, each...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 páginas
...equiangular triangle is also equilateral. PROP. VII. THEOR. UP0N the same base, and on the same side of 5 it, there cannot be two triangles that have their...those which are terminated in the other extremity. If it be possible, let there be two triangles ACB, ADB, upon the same base AB, and upon the same side...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volumen2

Charles Butler - 1814 - 528 páginas
..." 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 páginas
...• ent 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*; • 71 1. therefore, if the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 514 páginas
...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...one another, and likewise those which are terminated in'the other extremity: QED PROP. VIII. THEOR. IF two triangles have two sides of the one equal to...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 páginas
...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 - 1822 - 508 páginas
...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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