 | William Somerville Orr - Science - 1854 - 534 pages
...AB = CD ; Л equal chords, &c. QED PROPOSITION XY.— THEOREM. 27i« diameter is the greatest chord in a circle : and of all others, that which is nearer...: and the greater is nearer to the centre than the less. Let E be the centre of the circle ABCD, and let BC be nearer to it than FG : the diameter AD... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...straight line which joins them shall fall within the circle. 2. 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 one more remote : and the greater is nearer to the centre than the less. 3. If from any point without... | |
 | Euclides - 1855 - 270 pages
...bisection and touches them at these points, PROP. XV. THEOREM. 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 remole : and the greater is nearer to the centre than the ¡ess. Let AB СD be... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...centre of the circle is in the line which bisects the other. 7. The diameter is the greatest straight line in a circle; and, of all others, that which is...: and the greater is nearer to the centre than the less. BOOKS IV. VI. For Candidates for Honors. 1. INSCRIBE in a given circle a triangle equiangular... | |
 | Euclides - 1856 - 168 pages
...doubles of these or AB and CD are equal. LVIII.— EUCLID III. 15. The diameter is the greatest straight line in a circle, and of all others that which is...remote, and 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... | |
 | Euclides - 1860 - 288 pages
...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...; and 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... | |
 | War office - 1861 - 714 pages
...two pounds ; required the number of days he worked. Euclid. 1. 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 one more remote ; and the greater is nearer to the centre than the less. 2. In a circle the angle... | |
 | Euclides - 1861 - 464 pages
...>D. 15. 33. The diain. is the greatest st. line in a © ; and of all others that nearer to the cen. is always greater than one more remote : and the greater is nearer to the cen. than the less. SCH. The longest chord is the diam. ; the shortest through a giveu . , tint perp.... | |
 | Euclides - 1862 - 172 pages
...Therefore, equal straight lines, &c. Q, ED PROP. XV.— THEOEEM. The diameter is the greatest straight line in a circle, and, of all others, that which is...; and 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,... | |
 | Euclides - 1863 - 122 pages
...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... | |
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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... 
