 | Euclides - 1884 - Liczba stron: 434
...the segments of the other. PROPOSITION 15. THEOREMS. The diameter is the greatest chord in a circle; and of all others that which is nearer to the centre is greater than one more remote. Conversely : The greater chord is nearer to the centre than the less.... | |
 | 1885 - Liczba stron: 630
...and the remainders DBand CE are equal. 4. The diameter is the greatest straight line in a circle ; and of all others, that which is nearer to the centre...the greater is nearer to the centre than the less. Through a given point within a circle draw the least possible chord. Let ABCD be a circle, diameter... | |
 | Euclides - 1885 - Liczba stron: 340
...in a circle ; and of the others, the chord (CD) which is nearer to the centre is greater than (EF) one more remote, and the greater is nearer to the centre than the less. Dem. — 1. Join OC, OD, OE, and draw the perpendiculars OG, OH ; then because O is the centre, OA... | |
 | Euclid, John Casey - 1885 - Liczba stron: 340
...in a circle ; and of the others, the chord (CD) which is nearer to the centre is greater than (EF) one more remote, and the greater is nearer to the centre than the less. Dem. — 1. Join OC, OD, OE, and draw the perpendiculars OG, OH ; then because O is the centre, OA... | |
 | E. J. Brooksmith - 1889 - Liczba stron: 356
...rectangle AC, AD is equal to the square on CD. 6. The diameter is the greatest straight line in a circle, and of all others that which is nearer to the centre is greater than one more remote. Two circles cut one another, through a point of intersection draw a straight... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - Liczba stron: 538
...circle. (2) Of all others, that which is nearer to the centre is greater than one more remote. (3) The greater is nearer to the centre than the less. Let ABCD be a 0 of which AD is a diameter and E the centre; and of the two chords BC, FG let BC be the nearer to... | |
 | Euclid - 1892 - Liczba stron: 460
...others, that which is nearer to the centre is greater than one more remote: conversely, the greater chord is nearer to the centre than the less. Let ABCD be a circle, of which AD is a diameter, and E the centre ; and let BC and FG be any two chords, whose perp. distances from... | |
 | University of Toronto - 1900 - Liczba stron: 1164
...joining the centres of the two circles. 4. The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than the more remote ; and the greater is nearer to the centre than the less. (III. 15.) 5. In equal circles,... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - Liczba stron: 330
...chords, that which is nearer to the centre is greater than one more remote. Conversely, the greater chord is nearer to the centre than the less. Let ABCD be a circle of which AD is a diameter, and E the centre ; and let BC and FG be any two chords, whose perp. distances from... | |
 | Eldred John Brooksmith - 1901 - Liczba stron: 368
...rectilineal figure. 6. Prove that the diameter is the greatest straight line in a circle, and that, of all others, that which is nearer to the centre is always greater than one more remote. 7. Prove that the opposite angles of any quadrilateral figure inscribed in a circle are together equal... | |
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THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which... 
