 | Royal Scottish Society of Arts - Industrial arts - 1856 - 860 pages
...Prop. XX., Book III., Euclid, it is demonstrated that the angle at. the centre of a circle is double the angle at the circumference upon the same base that is upon the same part of the circumference. Let ABCDEF be a circular frame revolving on its centre at G, and let F be a point on the circumference... | |
 | Euclides - 1842 - 316 pages
...is the centre; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR, THE angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...that no other point which is not in CA, is the centre ; that is, the centre is in CA. PROP. XX. THEOR. The angle at the centre of a circle is double of the...the same base, that is, upon the' same part of the circumferB Let ABC be a circle, and BDC an angle at the centre, and BAC an angle at the circumference... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...half the arc CFD, since these three halves of arcs make up half the circumference. 919. PROP. XLIII. The angle at the centre of a circle is double of the angle at the dr. cuniference. D Let the angle at the circumference ADI> (fig. 275.) and the angle at the centre... | |
 | X. Y. Z. - Equations - 1843 - 124 pages
...:. r>d, and the point (a, b) is within the circle. 5*. In a circle the angle at the centre is double the angle at the circumference, upon the same base that is upon the same part of the circumference. (Euclid 20, 3.) Let the centre of the circle be the origin, then (r, o) (- r, o) will be the extremities... | |
 | Education - 1844 - 688 pages
...which there fall more than two equal straight lines to the circumference, that point is the centre. 10. The angle at the centre of a circle is double of the angle at the circumference upon the same base. 11. From a given circle, cut off a segment which shall contain an angle equal to a given rectilineal... | |
 | Church schools - 1844 - 456 pages
...sides, and two of the opposite angles of a four sided figure be equal, that figure is a parallelogram. 5. The angle at the centre of a circle is double of the angle at the circumference, when they stand on the same arc. 6. If the vertical angle of a triangle be bisected by a line, which... | |
 | Euclides, James Thomson - Geometry - 1845 - 382 pages
...the centre : that is, the centre is in C A. Therefore, if a straight line, &c. PROP. XX. THEOR. — The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. In the circle ABC, let BEC be an angle at the centre, and BAC an angle at the circumference, which... | |
 | Euclid - Geometry - 1845 - 218 pages
...centre ; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROPOSITION XX. THEOB. — The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
 | Euclides - 1845 - 546 pages
...the centre of the circle is in CA. Therefore, if a straight line, &c. QKI). PROPOSITION XX. THEOREM. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
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The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference. 
