 | Euclides - 1864 - 262 pages
...is equal to the arc DB. Therefore the given arc ADB is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right...ABCD be a circle, of which the diameter is BC, and center E, and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD, DC. Then... | |
 | Euclides - 1864 - 448 pages
...given arc ADB is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircte is a right angle ; but the angle in a segment greater...ABCD be a circle, of which the diameter is BC, and eenter E. and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD, DC. Then... | |
 | Henry White - 1864 - 156 pages
...line from a given point, either without or in the circumference, which shall touch a given circle. 7. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. • ALGEBRA. Set to candidates for the Admiralty who selected Algebra as a subject of Examination.... | |
 | J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...cut it at right angles, and if it cuts it at right angles it shall bisect it. Prop. 31. — Theorem. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. EUCLID, BOOK VI. Prop. 2. — Theorem. If a straight line be drawn parallel to one of the sides of... | |
 | Euclides - 1865 - 402 pages
...circumference DB ; •wherefore the circumference ADB is bisected in D. QEF 117 PROP. XXXI.— THEOREM. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. (References— Prop. I. 5, 17, 32 ; in. 22.) Let ABCD be a circle, of which the diameter is BC, and... | |
 | Robert Potts - 1865 - 528 pages
...XXX1. THEOREM. In a circle, the angle in a semicircle is a right angle ; but the angle in a legment greater than a semicircle is less than a right angle;...ABCD be a circle, of which the diameter is BC, and center E, and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD, DC. Then... | |
 | Queensland. Department of Public Instruction - Education - 1866 - 336 pages
...touches it on the inside or outside. 9. Prove that the angle in a semicircle is a right angle ; but that the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. ., 40 PROBLEMS. 10. Pivide a right angle into three equal angles. 11. In the base of a triangle, find... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...from a given point in one of its sides. 2. In a circle, 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. 3. Triangles, and also parallelograms, having the same altitude, are to one another, &c. 4. If a straight... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...arc AD is equal to the arc DB. Wherefore the given arc is bisected at DQEF PROPOSITION 31. THEOREM. In a circle the angle in a semicircle is a right angle;...than a right angle. Let ABCD be a circle, of which BC is .a diameter and E the centre ; and draw CA, dividing the circle into the segments ABC, ADC, and... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 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...than a semicircle is greater than a right angle. Let ABC be a © , O its centre, and BC a diameter. Draw AC, dividing the © into the segments ABC, ADC.... | |
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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. 
