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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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Papers for the schoolmaster, Volume 3

1867 - 336 pages
...and the least straight lines that can be drawn touching the former, and terminated by the latter. 3. The angle at the centre of a circle is double the angle at the circumference upon the same base, ie, upon the same part of the circumference. If any three points ABE, be taken...
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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852 - 470 pages
...double the squares of the half-line and the line made up of the half-line and the part produced. 10. The angle at the centre of a circle is double the angle at the circumference, upon the same base. 11. The angle between a tangent and any chord, is equal to the angle in the alternate...
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A Treatise on the Law of Patents for Useful Inventions in the United States ...

George Ticknor Curtis - Patent laws and legislation - 1854 - 718 pages
...triangle, the square of the hypothenuse is equal to the sum of the squares of the opposite sides ; that the angle at the centre of a circle is double the angle at the circumference ; or that similar triangles arc to each other in the duplicate ratio of their homologous sides. The...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...point which is the common vertex of two equal triangles having the given lines for their bases. 3. The angle at the centre of a circle is double the angle at the circumference upon the same base. If a circle touch internally another of twice the diameter, and from the centre...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...diameter, and of all others, that which is nearer the centre is always greater than that more remote. The angle at the centre of a circle is double the angle at the circumference, upon the same base, or upon the same arc of the circle. The angles in the same segment of a circle...
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 494 pages
...9. All angles formed In the same segment of a circle, or standing on the same arc, are equal. 10. An angle at the centre of a circle is double the angle at the circumference, if both stand on the same base. 11. Any angle in a semicircle is a right angle. 12. The angle formed...
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Practical Military Surveying and Sketching: With the Use of the Compass and ...

Alfred Wilks Drayson - Military topography - 1861 - 236 pages
...therefore be at the intersection of the two. This problem depends upon the fact, that upon the same base the angle at the centre of a circle is double the angle at the circumference. Suppose the angle APB to have been 40, BPC 30, the double of APB would be 80, then 180— 80=100....
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...geometrical progression. Hence prove the rule for turning a recurring decimal into a vulgar fraction. 7. 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. 8. In a right angled triangle,...
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The Projection and Calculation of the Sphere for Young Sea Officers Being a ...

S. M. Saxby - Nautical astronomy - 1861 - 140 pages
...propositions, besides definitions, axioms, and postulates, repetitions, &c.). 23. Euc. III. Prop. XX. — 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. In the triangle ADC, the side...
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Study of Steam and the Marine Engine for Young Sea Officers in H.M. Navy ...

S. M. Saxby - Marine engines - 1862 - 200 pages
...propositions, besides definitions, axioms, and postulates, repetitions, &c.) *27. Euc. III. Prop. XX.— 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. GEOMETRICAL THEOREMS. EDA equals...
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