| Robert Potts - Geometry, Plane - 1860 - 380 pages
...Therefore, the opposite angles, &c. QED PROPOSITION XXIII. 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, upon the same straight line AB, and upon the same side of it, let there... | |
| Euclides - 1862 - 140 pages
...BAD, BCD, are together equal to two right angles. PROPOSITION 23.— THEOREM. Upon the same straight line, and on the same side of it, there cannot be...two similar segments of circles, not coinciding with one another, (References— Prop. I. 16; III. 10; def. 11.) Hypothesis. — If it be possible, on the... | |
| Euclides - 1863 - 122 pages
...ACI) is equal to its interior angle, which is impossible (I. 16). Therefore upon the same straight line, and on the same side of it, there cannot be two similar segments of circles which do not ccincide. QED the point A may be on the point C. and the straight line AB upon the THOP.... | |
| Euclides - 1864 - 262 pages
...Therefore, the opposite angles, &c. QED PROPOSITION XXIII. THEOREM. Upon the tame 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... | |
| Euclides - 1865 - 402 pages
...Therefore, the opposite angles, &c. QED PROP. XXIII.— 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. (References — Prop. i. 16 ; in. 10, def. 11.) If it be possible, let the two similar... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...right angles. Wherefore, tlie opposite angles &c. QKD PROPOSITION 23. THEOREM. On the same straight line, and on the same side of it, there cannot be...two similar segments of circles, not coinciding with one another. If it be possible, on the same straight line AB, and on the same side of it, let there... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...right angles. Wherefore, the opposite angles &c. QED PKOPOSITION 23. THEOREM. On the same straight line, and on the same side of it, there cannot be...two similar segments of circles, not coinciding with one another. If it be possible, on the same straight line AB, and on the same side of it, let there... | |
| Robert Potts - 1868 - 434 pages
...Therefore, the opposite angles, &c. OED PROPOSITION XXIII. THEOREM. Upon the tame 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... | |
| Euclides - 1872 - 102 pages
...which contain equal angles. BOOK III. PROPOSITION XXIII. THEOREM. 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, on the same base AB, and on the same side of it, let there be two similar segments... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...equal, or which contain equal angles. PROPOSITION XXIII. THEOREM. 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, on the same base AB, and on the same side of it, let there be two similar segments... | |
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