 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.  Five Years in an English University - Page 348by Charles Astor Bristed - 1852Full view - About this book
 | John Playfair - Euclid's Elements - 1836 - 488 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...be two triangles, that have their sides which are terminal ed in one extremity of the base equal to one another, and likewise those which are terminated... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...Wherefore, if two angles, &c. Cor. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR.* UPON the same base, and on the same side of it, there...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. If it be possible, let... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...2. that .'. Aflisnot =/= AC, ie, that AB = AC. PROPOSITION VII. (Argument ad Absurdum.) Theorem. On the same base, and on the same side of it, there cannot be two triangles that have their sides terminated in one extremity of the base equal to each other, and likewise those terminated in the other... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...then, upon the same base EF, and upon the same side of it, there can be two triangles EOF, EGF,that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7.... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...equal to it. COR. — Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot he two triangles that have their sides which are terminated in one extremity of the base equal to one... | |
 | Robert Simson - Geometry - 1838 - 434 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...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. QED PROP. VIII. THEOR.... | |
 | Euclides - 1838 - 264 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...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. QE n. PROP. VIII. THEOR.... | |
 | Great Britain. Committee on Education - School buildings - 1853 - 1218 pages
...ability, will suffice for the highest class of certificates. Section 1. 1. Upon the same base and upon the same side of it there cannot be two triangles...terminated in one extremity of the base, equal to one another, and likewise those which are terminated at the other extremity. 2. The greater side of... | |
 | Euclides - 1840 - 82 pages
...them are also equal. COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base, and on the same side of it, there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other. PROP. VIII. THEOR.... | |
 | Euclides - 1840 - 192 pages
...— Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base (AB), and on the same side of it, there cannot be two triangles having their conterminous sides (AC and AD, BC and BD) at both extremities of the base, equal to each... | |
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