 | Euclides - 1846 - 272 pages
...21. B. 3.), and therefore the angle ABC is also less than a right angle. PART 3. — The angle ABC in a segment less than a semicircle is greater than a right angle. For assume in the opposite circumference any point D, and draw DA and DC. Therefore since in the quadrilateral... | |
 | John Playfair - Euclid's Elements - 1847 - 340 pages
...subdivisions, a given arc may be divided into four, eight, sixteen, &c. equal parts. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right...a semicircle is greater than a right angle. ' Let A BCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the... | |
 | Euclides - 1848 - 52 pages
...PROP. XXX. PROBLEM. To bisect a given circumference, that is, to divide it into two equal parts. PROP. XXXI. THEOREM. In a circle, the angle in a semicircle...less than a semicircle is greater than a right angle. PROP. XXXII. THEOREM. If a straight line touch a circle, and from the point of contact a straight line... | |
 | Great Britain. Council on Education - Education - 1848 - 532 pages
...different combinations that may be made of n different things, taking r of them together. Section 3. 1. In a circle the angle in a semicircle is a right angle,...less than a semicircle is greater than a right angle. 3. Similar triangles are to each other in the duplicate ratio of their homologous (or corresponding)... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...different combinations that may be made of n different things, taking r of them together. SECTION III. 1. In a circle the angle in a semicircle is a right angle,...less than a semicircle is greater than a right angle. 2. Describe a circle in a given triangle. 3. Similar triangles are to each other in the duplicate ratio... | |
 | Bengal (India) - 1848 - 520 pages
...— px + </=0 Geometry. 6. Any two sides of a triangle are together greater than the third side. 7. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. 8. In equal circles, angles, whether at the centres or circumferences, have the same ratio which the... | |
 | Great Britain. Committee on Education - Education - 1848 - 514 pages
...squares of the sides of the parallelogram. 3. In a circle, the angle in a semicircle is a right anyle ; but the angle in a segment greater than a semicircle is less than a right angle, and llie angle in a segment less than a semicircle is greater than a right angle. 4. To describe a circle... | |
 | Bengal council of educ - 1848 - 394 pages
...are equal to 2 right angles, .'. /_ ABC + /_ ADC = 2 right angles but ABC Z_ a right angle .'. ADC in a segment less than a semicircle is greater than a right angle. 8. \E ABCD and HLM are two equal circles, their centres being 0, G. AOB and HGK are two angles at the... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...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 AE, and produce... | |
 | 1850 - 400 pages
...from the centre; and those which are equally distant from the centre are equal to each other. • ,. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. 6. To describe an isosceles triangle, having each of the angles at the base double of the third angle.... | |
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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. 
