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" 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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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...wherefore the angle BDC is both equal to, and greater than the angle BCD ; which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base and on the same side of it, &c. QED PROPOSITION VIII. THEOREM. If two triangles have two sides of the one equal to two sides of...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...wherefore the angle BDC\s both equal to, and greater than the angle BCD ; which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base and on the same side of it, &c. QED PROPOSITION VIII. THEOREM. If two trirmgles have two sides of the one equal to two sides of...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...wherefore the angle BDC is both equal to, and greater than the angled CD; which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base and on the same side of it, &c. QED PROPOSITION Vm. THEOREM. lf two triangles have two sides of the one equal to two sides of the...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...needs no demonstration, for it is evident from inspection that the side AC is greater than its part AD. Therefore upon the same base and on the same side of it, &c. QED PROP. VIII.— THEOREM. If two triangles have two sides of the one equal to two sides of the...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 pages
...BA B c and AC shall coincide with DE and EF ; for if BA and AC do not coincide with ED and DF, then upon the same base and on the same side of it there can be two triangles, EDF and EGF, that have their sides which are terminated in one extremity of the...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 360 pages
...be greater than the same BCD ; which is impossible. The case in which the vertex of one triangle im upon a side of the other, needs no demonstration....that have their sides which are terminated in one extrem ity of the base equal to one another, and likewise those which are tormina ted in the other...
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Willis's Current notes

Willis's Current notes - Education - 1867 - 792 pages
...number of mangoes his basket contained ? Geometry. 1. Of the VII Proposition, the enunciation is : — " Upon the same base and on the same side of it, there cannot be two triangles, &c." What is the use of saying on tht same side ? Demonstrate the above Proposition. Babu Blioodeb...
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Examination papers collected by A. Clark as a student and as an examiner

1867 - 224 pages
...magnitudes said to coincide? What name is given to a triangle which has three unequal sides ? 2. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...&c. QED Corollary. Hence every equiangular triangle is also equilateral. PROPOSITION 7. THEOREM. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...&c. QED Corollary. Hence every equiangular triangle is also equilateral. PROPOSITION 7. THEOREM. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise...
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