 | James Mitchell - 1823 - 666 σελίδες
...semi-circle, or standing upon a semi-circle or diameter. An ancle in a semi-circle, is a right-angle. An angle in a segment, greater than a semi-circle, is less than a right-angle. An angle in a segment, less than a semi-circle, is greater than a right-angle. ANGULAR,... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...two right angles. THEOREM 37. 94. An angle ABD, in a semi-circle, is a right angle ; an angle BAD, in a segment greater than a semi-circle, is less than a right angle ; and an angle, BED, in a segment less than a semi-circle, is greater than a right angle. Produce AB... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...done. Proposition XXXI. Theorem. In a circle, the angle in a semicircle is a right angle ; but 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. Let ÀBCD be a... | |
 | Nathaniel Bowditch - 1826 - 764 σελίδες
...are .N equal to each other ; for they are all measured by the same arch, viz. half the arch AB. XLII. An angle in a segment greater than a semicircle is less than a right angle. Thus if ABC be a segment greater than a semicircle, the arch AC on which it stands must be less than a semicircle,... | |
 | Euclides - 1826 - 226 σελίδες
...bisected. QEF PROPOSITION XXXI. THEOREM. In a circle the angle in a semicircle is a right angle, also that in a segment greater than a semicircle is less than a right angle, and that in a segment less than a semicircle is greater than a right angle, and moreover the angle... | |
 | Euclid - 1826 - 234 σελίδες
...bisected. QEF PROPOSITION XXXI. THEOREM. In a circle the angle in a semicircle is a right angle, also that in a segment greater than a semicircle is less than a right angle, and that in a segment less than a semicircle is greater than a right angle, and moreover the angle... | |
 | George Lees - 1826 - 276 σελίδες
...VIII. THEOREM. . . i In a circle, the angle BAC in a semicirle is a right angle ; but, the angle ABC in a segment greater than a semicircle, is less than a right angle ; and the angle ADC, in, a segment, less than a semicirle, is greater than a right angle. Produce BA... | |
 | Robert Simson - 1827 - 546 σελίδες
...was to be done. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle ; but 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. Let ABCD be a circle,... | |
 | Pierce Morton - 1830 - 584 σελίδες
...semi-circumference, that is, by a quadrant. Cor. 2. (Eue. iii. 31 second part of.) The angle, which is in a segment greater than a semicircle, is less than a right angle ; and the angle, which is in a segment less than a semicircle, is greater than a and let the diameters... | |
 | Euclid - 1835 - 540 σελίδες
...III. PROP. XXXI. THEOR. ^ /— ' In a circle, the angle in a semicircle is a right angle ; but 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. Let ABCD be a circle,... | |
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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. 
