 | Robert Simson - Trigonometry - 1827 - 546 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 can- See N. not be two triangles that have their sides which are terminated in one extremity of the... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...angles, the lines AI, BD, produced, will meet.' The other is from Simson's Euclid, prop. 7, b. 1 . ' Upon the same base and on the same side of it, there...those which are terminated in the other extremity.' Now we presume there can be no doubt, which of these two methods is best adapted to the conception... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...right angles, the lines AI, BD, produced, will meet.' The other is from Simson's Euclid, prop. 7, b. 1. 'Upon the same base and on the same side of it, there...those which are terminated in the other extremity.' Now we presume there can be no doubt, which of these two methods is best adapted to the conception... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...CA, AB are all equal to one another. PROPOSITION VII. THEOREM. — Upon the same given straight line and on the same side of it, there cannot be two triangles...their sides which are terminated in one extremity of it equal to one another, and also those which are terminated in the other See Note. extremity. For... | |
 | Euclid - 1835 - 540 pages
...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 imposa 7. 1. sible " ; therefore, if the... | |
 | Mathematics - 1836 - 488 pages
...one another, the sides which subtend, or are opposite to them, are also equal to one another. VII. Upon the same base, and on the same side of it, there...those which are terminated in the other extremity, equal to one another. VIII. If two triangles have two sides of the one equal two sides of the other,... | |
 | 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... | |
 | 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. 1.) ; therefore, if the... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...FG ; then, upon the same base EF, and upon the same side of it, there would be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in * Or, if the three aides of one triangle be equal to the three sides of another,... | |
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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. 
