 | John Playfair - 1833 - Liczba stron: 346
...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 - Liczba stron: 518
...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 - Liczba stron: 544
...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 - Liczba stron: 488
..." 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 - Liczba stron: 410
...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 - Liczba stron: 290
...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 - Liczba stron: 112
...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 - Liczba stron: 82
...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 - Liczba stron: 192
...— 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 - Liczba stron: 378
...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... 
