| John Playfair - Euclid's Elements - 1806 - 311 pages
...opposite angles, &c. Q. E, D. ^ PROP. XXIII. THEOR. Book in. UPON the same straight line, and upon **the same side of it, there cannot be two similar segments of circles, not coinciding with each other.** If it be possible, let the two similar segments of circles, ACB, ADB be upon the same side of the same... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...angles, Sec. QE I). *— y~* PROP. XXIII. THEOR. UPON the same straight line, and upon the same See N. **side of it, there cannot be two similar segments of circles not coinciding with** one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the... | |
| Euclid - Geometry - 1810 - 518 pages
...opposite angles, &c. QED PROP. XXIII. THEOR. UPON the same straight line, and upon the same See Noteside **of it, there cannot be two similar segments of circles, not coinciding with** one another. If it be possible, let the two similar segments of circles, viz. ACB, ABD be upon the... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...circle, are together equal to two right angles. Prop. XXIII. Theor. Upon the same straight line, and upon **the same side of it, there cannot be two similar segments of circles, not coinciding with** one another. Prop. XXIV. Tlieor. Similar segments of circles Upon equal straight lines, are equal to... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...angles. Therefore the opposite angles, &c. QED PROP. XXIII. THEOR. Upon the same straight line, and upon **the same side of it, there cannot be two similar segments of circles, not coinciding with** one another. If it be possible, let the two similar segments of circles, vie. ACB, ADB, be upon the... | |
| Euclides - 1821
...absurd. C'or. Hence every equiangular triangle is equilateral ; vide, Elrington. PROP. 7. THEOR. i **On the same right line and on the same side of it there cannot be two** triangles formed whose conterminous sides are equal. If it be possible that there can, 1st, let the... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...Therefore, the opposite angles, &c. QED Propotition XXIll. Theorem. Upon the same straight line, and upon **the same side of it, there cannot be two similar segments of circles, not coinciding with** one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...Therefore, the ppposite angles, &c. QED PROP. XXIII. THEOR. (See N. Upon the same straight line, and upon **the same side of it, there cannot be two similar segments of circles, not coinciding 'with** one another. If it be possible, upon the same straight line AB, and upon the same side of it, let there... | |
| Euclid, Robert Simson - Geometry - 1829 - 516 pages
...angles. Therefore the opposite angles, &c. QED PROP. XXIII. THEOR. UPON the same straight line, and upon **the same side of it, there cannot be two similar segments of circles, not coinciding with** one another.* Ifitbe possible,letthe two similarsegments of circles, viz. ACB, ABD be upon the same... | |
| Euclides - 1833
...whole, which is absurd. Cor. Hence every equiangular triangle is equilateral ; vide Elrington. PROP. 7, **THEOR. On the same right line and on the same side of it, there cannot be two** triangles formed whose conterminous sides are equal. If it be possible that there can, 1st. let the... | |
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