 | John Playfair - 1806 - 320 σελίδες
...arch ADB e Cor. 1. 5. is bisected in D. Which was to be done. Book in PROP. XXXI. THEOR. IN a circle the angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment Jess than... | |
 | Sir John Leslie - 1817 - 456 σελίδες
...hence another mode of drawing a parallel through a given point to a given straight line. PROP. XIX. THEOR. The angle in a semicircle is a right angle,...in a greater segment is acute, and the angle in a smalkr segment is obtuse. Let ABD be an angle in a semi-circle, or that stands on the semicircumference... | |
 | Sir John Leslie - 1820 - 482 σελίδες
...hence another mode of drawing a parallel through a given point to a given straight line. PROP. XIX. THEOR. The angle in a semicircle is a right angle,...is obtuse. Let ABD be an angle in a semicircle, or standing on the semicircumference AED ; it is a right angle. For ABD, being an angle at the circumference,... | |
 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...(XXVIII), and therefore the given arc is bisected in B. PROPOSITION XXXI. THEOREM. (389) In a circle the angle in a semicircle is a right angle, the angle in a segment greater than a semicircle is acute, and the angle in a segment less than a semicircle is obtuse.... | |
 | Euclides - 1833 - 304 σελίδες
...connecting lines, are = ; .-. the arcs, which they subtend, are = ; .-., &c. PROP. 31. THEOR. In a circle, the angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is an acute angle ; and the angle in a segment less than a semicircle... | |
 | 1835 - 684 σελίδες
...they stand -wi cor. 86 (y) Angles in the same segment of a circle are equal to one another 8(i (A) The angle in a semicircle is a right angle ; the angle in a segment, which is greater than a semicircle, is less than a right angle ; and the angle in a segment,... | |
 | Euclides - 1840 - 82 σελίδες
...subtending equal arches are equal. PROP. XXX. PROB. To bisect a given arch of a circle. A 3 PROP. XXXI. THEOR. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle, is an acute angle; and the angle in a segment less than a semicircle,... | |
 | London univ - 1846 - 326 σελίδες
...equations : Sx+4 30-2*7*— 14 ' 5 ~ x-6 ~ 10 ' (2.) &— xy=48y\ xy— y*=3x J ' (3.) *+— a«=0. 9. The angle in a semicircle is a right angle, the angle in a segment greater than a semicircle is less than a right angle, and the angle in a segment less than... | |
 | Harvey Goodwin - 1851 - 196 σελίδες
...square and one side of a rectangle which is equal to the square, find the other side. 3. In a circle, the angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than... | |
 | Great Britain. Committee on Education - 1855 - 976 σελίδες
...centre, it shall cut it at right angles ; and if it cuts it at right angles it shall bisect it. 7. The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle : and the angle in a segment less than... | |
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... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral... 
