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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

## First Public Examination in Literis Graecis Et Latinis

...rectangle contained by the whole and one of the parts may be equal to the square on the other part. 10. In a circle the angle in a semicircle is a right angle...less than a semicircle is greater than a right angle. 11. Inscribe an equilateral and equiangular hexagon in a given circle. 12. Equal triangles which have...

## Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...the inscribed quadrilateral and the opposite extenor angle meet in the circumference. Section III. 1. In a circle, the angle in a semi-circle is a right...than a semi-circle is greater than a right angle. The greatest rectangle that can be inscribed in a circle is a square. , 2. From a given circle to cut...

## The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 266 pages
...therefore BC is equal (I. 7) to EF. Proposition 21. Theorem.—The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle,...than a semicircle, is greater than a right angle. ADC, and join BA, AD, DC; the angle in the semicircle BA C is a right angle; the angle in the segment...

## Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

Euclides, James Hamblin Smith - Euclid's Elements - 1879 - 349 pages
...the radius. PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle ; and the angle in a segment greater than a semicircle is...less than a right angle ; and the angle in a segment lest than a is greater than a right angle. Let ABC be a 0, O its centre, and BC a diameter. Draw AC,...

## Military examinations. Mathematical examination papers, set at entrance to ...

...The angle at the centre of a circle is double the angle at the circumference upon the same base. 4. In a circle the angle in a semicircle is a right angle...less than a semicircle is greater than a right angle. Circles are described on the sides of a triangle as diameters. Show that their points of intersection...

## American Practical Navigator

Nautical astronomy - 1880
...are ei/ttat to each other ; for they are all measured by the same arc, viz. half the arc AR XLH. 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 less than...

## The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...when the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle. [III. 31. Therefore, conversely, if the given triangle be acuteangled, the centre of the circle falls...

## The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...hke manner, by drawing a straight line from the point A, within the angle BAC, it may be shown that the angle in a segment greater than a semicircle is less than a rigbt angle. l,-Itrase. — To draw a perpendicular to a straight line from one of its extremities...