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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. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 79
by Euclides - 1816 - 528 pages
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1847 - 317 pages
...by successive 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...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...
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General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848
...— 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...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...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...
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Report of the Committee of Council on Education (England and Wales ..., Issue 1

Great Britain. Council on Education - Education - 1848
...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)...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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 is a right...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...
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Minutes of the Committee of Council on Education, with Appendices, Volume 1

Great Britain. Committee on Education - 1848
...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...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848
...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...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 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...
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The Calendar of King's College, London

1850
...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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