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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, equal to one another. "
Examination papers used at the examinations for direct commissions [&c.]. - Pagina 12
door War office - 1861 - 12 pagina’s
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 pagina’s
...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 - 311 pagina’s
...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 - 518 pagina’s
...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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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...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
...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 ..., Volume 2

Charles Butler - 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pagina’s
...• 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 pagina’s
...&c. Q, ED 33 " " " ~ 0 COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there...those which are terminated in the other extremity, equal to one another. Let there be two triangles ACB, ADB, upon the same base AB, and upon the same...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pagina’s
...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 - 1821 - 516 pagina’s
...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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