| Euclides - 1840 - 192 pages
...Proposition is introduced for the sake of proving the Eighth. It amounts to this, that on the same straight line, and on the same side of it, there cannot be two isosceles triangles, having the vertex of each outside of the other. It is shown by the indirect method,... | |
| Euclides - Geometry - 1841 - 378 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. I 2 If it be possible, upon the same straight line AB, and upon the same side of it, let... | |
| Euclides - 1842 - 316 pages
...to ADC by the proposition. Therefore, &c. 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, viz. ACB, ADB be upon the... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...cannot be inscribed in a circle. 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, viz. ACB, ADB, be upon the... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...angles. Take away CBA, and there remains CBE equal to CDA. PROP. XXIII. THEOR. — 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. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the... | |
| Euclides - 1845 - 546 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 AJi, and upon the same side of it, let... | |
| Euclid - Geometry - 1845 - 218 pages
...right angles. ' St. 1. t 11.3. PROPOSITION XXIII. THEOB. — 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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...angles, cannot be inscribed in a circle. 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, viz. ACB, ADB, be upon the... | |
| Euclides - 1846 - 292 pages
...Wherefore, The opposite angles S;c. Qi•..i>. 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 two similar segments of circles, viz. ACB, ADB, be upon the same... | |
| Euclides - 1848 - 52 pages
...are together equal to two right angles. 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. PROP. XXIV. THEOREM. Similar segments of circles upon equal straight lines, are equal... | |
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