| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...CB, 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 that have their sides which are terminated in one extremity of it equal to one another, and... | |
| 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... | |
| John Playfair - Geometry - 1836 - 148 pages
...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... | |
| 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.... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...Z s BAD + DCS = 2 rt. Z *. PROPOSITION XXIII. (Argument ad absurdum.) Theorem. On the same straight line, and on the same side of it, there cannot be...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... | |
| Euclid, James Thomson - Geometry - 1837 - 410 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, A DB, be upon the... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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... | |
| John Playfair - Euclid's Elements - 1837 - 332 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 - 1838 - 264 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, upon the same straight line AB, and upon the same side of it, let there... | |
| Euclides - 1840 - 82 pages
...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 each other. PROP. XXIV. THEOR. Similar segments of circles upon equal straight fines are equal to each other. PROP.... | |
| |