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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, containing the first six books, with a selection of ... - Σελίδα 112
των Euclides - 1874
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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 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...

## The London University Calendar

London univ - 1846 - 326 σελίδες
...(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 semicircle is greater than a right angle. 10. Inscribe in a given circle an equilateral and equiangular hexagon. 1 1 . Define the sector of a...

## The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 864 σελίδες
...are ernial to each other ; for they are all measured by the same arc, viz. half the arc 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 arc AC on which it stands must be 1еяч...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 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...

## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 σελίδες
...if the centre fall without the triangle, the angle opposite to the side beyond which it falls, being in a segment less than a semicircle, is greater than a right angle : Wherefore, if the given triangle be acute-angled, the centre of the circle will fall within it ;...

## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 σελίδες
...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...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1847 - 340 σελίδες
...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...circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the segments ABC, ADC, and join BA, AD, DC ; the angle in the semicircle...

## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 σελίδες
...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 is...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...

## General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848 - 520 σελίδες
...— 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...

## Report of the Committee of Council on Education (England and Wales ..., Τεύχος 1

...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)...