 | Euclides - 1860 - 288 pages
...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 to the centre...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... | |
 | War office - 1861 - 714 pages
...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
...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 nearer to the centre...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 - 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 and EC;... | |
 | Henry White - 1864 - 156 pages
...made up of the half and the part produced. 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. 5. A segment of a circle being given, describe the circle of which it is the segment. 6. If the outward... | |
 | Euclides - 1865 - 402 pages
...one another ..... m. 14. 4. The diameter is the greatest straight line in a circle ; and of the rest, that which is nearer to the centre is always greater than one more remote ; and conversely, the greater is nearer to the centre than the less .,...,. m. 15. 5. In equal circles, equal... | |
 | Civil service - 1866 - 270 pages
...made up of the half and the part produced. 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. 5. A segment of a circle being given, describe the circle of which it is the segment. 6. If the outward... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...straight lines &c. QED PROPOSITION 15. THEOREM. The diameter is the greatest straight line in a circle ; and, of all others, that which is nearer to the centre...centre than the less. Let ABCD be a circle, of 'which AD is a diameter, and E the centre ; and let BC be nearer to the centre than FG : AD shall be greater... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...PROPOSITION 15. THEOREM. The diameter is the greatest straight line in a circle ; and, of all otfters, that which is nearer to the centre is always greater...centre than the less. Let ABCD be a circle, of which AD is a diameter, and E the centre ; and let BC be nearer to the centre than FG : AD shall be greater... | |
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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... 
