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

Sandhurst roy. military coll - 1880 - 68 pages
...circumference of the other. Show that the square on the common chord is three times the square on a radius. 3. 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 ; but the angle in a...
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Lay Sermons

John Stuart Blackie - Christianity - 1881 - 410 pages
...necessity of mathematics, — is more certain. It is not more certain that two and two make four, or that the angle at the centre of a circle is double the angle at the circumference, generation of sophists, more anxious to show their own cleverness by making petty objections, than...
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The Competitor, Volumes 3-4

1883 - 248 pages
...in this line. Hence show how to describe a circle of which a portion only is given. 62 7. Prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. Deduce that the angle in a segment greater than a semicircle is less than...
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A Treatise on Marine Surveying: Prepared for the Use of Younger Naval ...

J. L. Robinson - Boats and boating - 1882 - 356 pages
...triangle are equal. (2) The three angles of a triangle are together equal to two right angles. (3) The angle at the centre of a circle is double the angle at the circumference standing on an equal arc. (4) The opposite angles of a quadrilateral inscribed in a circle are together...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 292 pages
...right-angled triangles ; hence, AK is equal to AB. GEOMETRY.— BOOK III. Proposition 16. Theorem. — 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 ABC be a circle, BDC the...
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Gibson's London matriculation guide, by J. Gibson [and others].

1882 - 376 pages
...its sides, find the locus of its vertex, and state when the locus becomes impossible. 6. Prove that the angle at the centre of a circle is double the angle at its circumference. on the same arc. 7. AB is any chord of a circle, and AC is the tangent at the point...
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Calendar of Dalhousie College and University

Dalhousie University - 1885 - 230 pages
...BDa + BF2 = 2 D17 + 2 CB2. 3. One circle cannot touch another internally in more points than one. 4. The angle at the centre of a circle is double the angle at the circumference standing on the same arc. Prove this, in the case where the lines containing the second angle are on...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...part of the other, unless TB go through O. /. TB must go through O. Proposition 20. • THEOREM — The angle at the centre of a circle is double the angle at the circumference, standing on the same arc. A Let BC be an arc of a O, on which stand BOC at centre O, A and BAG at circumf....
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Practical Plane and Solid Geometry, Including Graphic Arithmetic

Isaac Hammond Morris - Geometry, Plane - 1890 - 430 pages
...first triangle. (Art.) Note. — Bisect the sides, and find the centre for the circumscribing circle. The angle at the centre of a circle is double the angle at the circumference, standing upon the same base. (Eue. ш. 20.) 7. Draw a triangle, two of whose sides are 2'5" and 8"...
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Transactions of the Institution of Naval Architects, Volume 38

Royal Institution of Naval Architects - Naval architecture - 1897 - 438 pages
...from the bisecting line the amount * X = Q sin 2 (q + 45" -!•) = Q cos (2 g - 2 ,|,). (17) Because the angle at the centre of a circle is double the angle at the circumference, standing upon the same arc, $ X is therefore the varying factor in the second line of (9). For the...
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