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" The angle at the centre of a circle is double the angle at the circumference on the same arc. "
Elementary Plane Geometry: Inductive and Deductive - Página 86
por Alfred Baker - 1903 - 144 páginas
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - 1867 - 283 páginas
...the arc AEB ; and thus, having equal measures, they are equal to each other (ax. 11). THEOREM XI. An angle at the centre of a circle is double the angle at the circumference, when both stand on the same arc. Let C be an angle at the centre C, and D an angle at the circumference,...
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The elements of mechanism

Thomas Minchin Goodeve - 1870
...equal to CP or c R ; draw any fixed diameter A c B, and join A R. Then it is proved in Euclid that the angle at the centre of a circle is double the angle at the circumference when Fig. 248. both angles stand upon the same arc, that is<lPCA = 2Z.PRA or the angular velocity of...
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Four Phases of Morals: Socrates, Aristotle, Christianity, Utilitarianism

John Stuart Blackie - 1871 - 414 páginas
...present, or to come. When I say that all the angles of a triangle are equal to two right angles, or that the angle at the centre of a circle is double the angle at the circumference, I prove this from certain necessary relations of lines to lines drawn under conditions of which my...
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An Introduction to the Practical and Theoretical Study of Nautical Surveying

John Knox Laughton - 1872 - 166 páginas
...DA, will pass through B. The segment A GB is the segment required. It is proved (Euclid III. 20) that the angle at the centre of a circle is double the angle at the circumference, standing on the same base, or part of the circumference ; that is, the angle ADB is double of the angle...
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Annual Register of the United States Naval Academy ..., Volúmenes25-32

United States Naval Academy - 1874
...iu E and D, prove that e straight lines BD, DE, and E С will be equal to each other. 2. Prove that the angle. -at the centre of a circle is double the angle at the circum•ence on the same arc. AR and CD are two chords of a circle which intersect, зеп produced,...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...sector of a circle is the figure contained by two radii and the arc they intercept. • THEOREM XXX. The angle at the centre of a circle is double the angle at the circumference on the same arc. There are three cases to consider, according as the centre of the circle is (i) on...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...ABC, therefore they are equal (P. 36). Because the angles at the circumferences are' equal and because the angle at the centre of a circle is double the angle at the circumference, therefore it could be proved, that the angles at G and H standing upon the equal arcs EF and BC are...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880
...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 - 1881 - 349 páginas
...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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A Treatise on Marine Surveying: Prepared for the Use of Younger Naval ...

J. L. Robinson - 1882 - 307 páginas
...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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