 | Euclides - 1884 - 434 pages
...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.... | |
 | Education - 1885 - 630 pages
...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 - 340 pages
...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 - Euclid's Elements - 1885 - 340 pages
...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 - Mathematics - 1889 - 356 pages
...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 - 538 pages
...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 - Geometry - 1892 - 460 pages
...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 - 1164 pages
...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 - Euclid's Elements - 1900 - 330 pages
...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 - Mathematics - 1901 - 368 pages
...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... 
