| 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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