| Euclides - 1855
...circle passes through all the points of bisection and touches them at these points, PROP. XV. THEOREM. **The diameter is the greatest straight line in a circle...all others. that which is nearer to the centre is** greater than one more remole : and the greater is nearer to the centre than the ¡ess. Let AB СD be... | |
| Euclides - 1856
...CG and AF to C G. Therefore the doubles of these or AB and CD are equal. LVIII.— EUCLID III. 15. **The diameter is the greatest straight line in a circle,...the greater is nearer to the centre than the less.** Let A BCD (Fig 46) be a circle of which' the diameter is AD and centre E, and let BC, FG be any straight... | |
| Cambridge univ, exam. papers - 1856
...other part. 10. If two circles touch one another internally, they shall not have the same centre. 11. **The diameter is the greatest straight line in a circle;...the greater is nearer to the centre than the less.** 12. The opposite angles of any quadrilateral figure described in a circle, are together equal to two... | |
| War office - 1858 - 12 sider
...square of half the line, is equal to the square of the line made up of the half and part produced. 2. **The diameter is the greatest straight line in a circle, and of** the rest that which is nearer to the centre is greater than one more remote. Draw a line in a circle... | |
| Euclides - 1860
...then, if A = C, B = D; or, if A^C, B./D. PROPOSITION XV. THEOREM. The diameter is the greatest chord **in a circle; and, of all others, that which is nearer...the greater is nearer to the centre than the less.** Given a circle ABCD, of which the diameter is AD, and the centre E ; and BC a chord nearer to the centre... | |
| Robert Potts - 1860 - 361 sider
...wherefore AB is equal to CD. (ax. 6.) Therefore equal straight lines, &c. QED PROPOSITION XV. THEOREM. **The diameter is the greatest straight line in a circle ; and of** the rest, that which is nearer to the center is always greater than one more remote : and conversely... | |
| War office - 1861 - 12 sider
...the end of the time he had to receive two pounds ; required the number of days he worked. Euclid. 1. **The diameter is the greatest straight line in a circle...which is nearer to the centre is always greater than** the one more remote ; and the greater is nearer to the centre than the less. 2. In a circle the angle... | |
| Euclides - 1862
...CG ; wherefore AB Is equal to CD. Therefore, equal straight lines, &c. Q, ED PROP. XV.— THEOEEM. **The diameter is the greatest straight line in a circle,...the greater is nearer to the centre than the less.** (References— Prop. i. 12, 20; in. def. 5.) Let ABCD be a circle, of which the diameter is AD, and... | |
| Euclides - 1863
...circle (ABCD); end, of all others, that (BC) ,rlrich is nearer to the centre (E) is greater than (l'"G) **one more remote: and the greater is nearer to the centre than the less.** Because AE is equal (I. Def. 15) to EB. and ED to EC ; therefore AD is equal (I. Ax. 2) to EB and EC;... | |
| Henry White - 1864
...is equal to the square of the straight line which is made up of the half and the part produced. 4. **The diameter is the greatest straight line in a circle;...the greater is nearer to the centre than the less.** 5. A segment of a circle being given, describe the circle of which it is the segment. 6. If the outward... | |
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