 | Euclid - 1835 - 540 pages
...opposite angles," &c. QED 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... | |
 | Mathematics - 1836 - 488 pages
...described in a circle, are together equal to two right angles. XXIII. 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. XXIV. Similar segments of circles upon equal straight lines are equal to one another.... | |
 | John Playfair - Geometry - 1836 - 148 pages
...right angles. Therefore, the opposite angles, &c. QED PROP. XV. THEOR. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with another. • If it be possible, let the two similar segments of circles, viz. ACB, ADB be upon the... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...= 2 rt. Z *. PROPOSITION XXIII. (Argument ad absurdum.) Theorem. On the same straight line, and on the same side of it, there cannot be two similar segments of circles not coinciding with each other. Steps of the Demonstration. Suppose that the segments ACB, ADB are similar, and on the same right line... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...two right 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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...be shown to he equal to two right angles. i 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. because the circle ACB cuts the circle ADB in the two points A, B, they cannot cut one... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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, A DB, be upon the... | |
 | Euclides - 1838 - 264 pages
...right 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, upon the same straight line AB, and upon the same side of it, let there... | |
 | Euclides - 1840 - 82 pages
...a 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...segments of circles not coinciding with each other. PROP. XXIV. THEOR. Similar segments of circles upon equal straight fines are equal to each other. PROP.... | |
 | Euclides - Geometry - 1841 - 378 pages
...right 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... | |
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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 same side of the same straight... 
