 | Robert Simson - 1838 - 434 σελίδες
...DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce... | |
 | Euclides - 1840 - 192 σελίδες
...Z. ABD is less than a right angle a Prop. 32). But L ABD=Z. AFD (m. Prop. 2i) ; therefore Z. AFD or the angle in a segment greater than a semicircle is...less than a right angle. And the angle in a segment AGD less than a semicircle, is greater than a right angle. For take any point G in the segment, and... | |
 | Euclides - 1840 - 82 σελίδες
...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, is an obtuse angle. PROP. XXXII. THEOR. If a straight line touches a circle, and from the point of contact... | |
 | Euclides - 1841 - 378 σελίδες
...Which was to be done. PROP. XXXI. THEOR. In, a circle, the angle in a semicircle is a rig hi angle; the angle in a segment greater than a semicircle is...than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E; and draw CA, dividing the circle into... | |
 | John Playfair - 1842 - 332 σελίδες
...DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC. which is less than a semicircle, is greater than a right angle. Join AE, and produce... | |
 | Euclides - 1842 - 316 σελίδες
...AD, DC: the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join A, E, and produce... | |
 | Cambridge univ, exam. papers - 1843 - 50 σελίδες
...equal to one another, and the diameter bisects them, that is, divides them into two equal parts. 2. In a circle the angle in a semi-circle is a right...than a semi-circle is greater than a right angle. 3. What sum must be invested in the 3 per cent, stock at 94J, to yield an annual income of £500 ?... | |
 | John Playfair - 1844 - 338 σελίδες
...is equal (4. 1.) to the base BD. But equal straight lines cut off equal arcs. (28. 3.) the greater equal to the greater, and the less to the less ; and...than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the... | |
 | Euclides - 1845 - 546 σελίδες
...circumference DB. Therefore the given circumference is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right...a segment greater than a semicircle is less than a rig/it angle; and \he angle in a segment less than a semicircle is greater than a right angle. Let... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...to AB. PROPOSITION LII. — THEOREM. An angle ADB in a semicircle is a right angle, and an angle DBA in a segment greater than a semicircle is less than a right angle, and an angle AED in a segment less than a semicircle is greater than a right angle. and v DC=CB, the ZCBD... | |
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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. 
