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" The angle at the centre of a circle is double the angle at the circumference on the same arc. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 128
by Euclides - 1821
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Annual Report of the Public Schools of the Province of British Columbia

British Columbia. Superintendent of Education - 1893 - 814 pages
...figure. 4. One circle cannot touch another, either externally or internally, in more than one point. 5. The angle at the centre of a circle is double the angle at the circumference, standing on the same arc. 6. About a given circle to describe a triangle, equiangular to a given triangle....
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 482 pages
...Theorem ; in consequence of which, it is said, lie offered a hecatomb to the gods. THEOREM VIII. An angle at the centre of a circle is double the angle at the circumference, when both stand on the same arc. Let ABC be a circle, and BDC an angle at the centre, and BAG an angle at...
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Logical Sequence in Plane Geometry

18 pages
...diameter. seg. The figure bounded by a chord of a circle and either arc cut off by it is called a segment. The angle at the centre of a circle is double the angle at the circumference standing on the same arc. The case of reflex angle is not necessary for the logical sequence nor for...
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The Contents of the Fifth and Sixth Books of Euclid (with a Note on ...

Euclid - Euclid's Elements - 1908 - 196 pages
...then arc CD : arc EF < - . r .-. CAD : EBF= arc CD : arc EF. [Prop. 13. [Prop. 13. [Art. 46. (ii) An angle at the centre of a circle is double the angle at the circumference standing on the same arc. Hence the ratio of two angles at the centre of the same or of equal circles...
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The Bombay University Calendar

University of Bombay - 1902 - 1102 pages
...any chord of the greater circle drawn from the point of contact is b.sected by the lesser circle. 6. The angle at the centre of a circle is double the angle at the circum- 1 3 f erence, when the angles stand on the same arc. Two circles whose centres are A and В...
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An Introduction to Engineering Mathematics

288 pages
....ADB is said to stand on the arc ACB, whilst .ACB stands on the arc ADB. 173. Proposition 10. An angle at the centre of a circle is double the angle at the circumference standing on the same arc. Let AEB (Fig. 141 (a)) be an arc of a circle of which 0 is the centre, and...
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