 | John Playfair - 1833 - 346 pagina’s
...1.) to the 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 Bide of the other, needs no demonstration. Therefore, upon the same base, and on the same side of it,... | |
 | Euclides - 1834 - 518 pagina’s
...triangle is also equilateral. PROPOSITION VII. See N. THEOR. — Upon the same base, and on the mine side of it, there cannot be two triangles that have their sides which arc terminated in one extremity of the base, equal to one a not her, and likewise those which are terminated... | |
 | Robert Simson - 1835 - 544 pagina’s
...a to the 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...base, and on the same side of it, there cannot be two trianyles that have tfieir sides which are terminated in one extremity of the base equal to one another,... | |
 | John Playfair - 1836 - 488 pagina’s
..." to the 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...demonstration. Therefore, upon the same base, and on thf* same side of it, there cannot be two triangles that have their sides which are terminated in one... | |
 | Euclid, James Thomson - 1837 - 410 pagina’s
...equal (I. 5.) to 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...side of the other, needs no demonstration. Therefore on the same base, and on the same side of it, there cannot be two triangles that have their sides which... | |
 | Andrew Bell - 1837 - 290 pagina’s
...equal to the 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 no demonstration. PROPOSITION VIII. THEOREM. If two triangles have two sides of the one equal to two sides of the other,... | |
 | Euclides - 1837 - 112 pagina’s
...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... | |
 | Euclides - 1840 - 82 pagina’s
...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 pagina’s
...— 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... | |
 | Euclides - 1841 - 378 pagina’s
...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 thai have their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
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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... 
