Books Books 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 ## A Treatise on Surveying: In which the Theory and Practice are Fully ...

Samuel Alsop - Surveying - 1865 - 440 pages
...angled triangle is equal to the sum of the similar figures similarly described on the sides. (31.6.) 83. The angle at the centre of a circle is double the angle at the circumference on the same base. Thus, the angle at 0 (Fig. 11) is double e'ther D or E. (20.3.) 84. Angles in the... ## Report on Education in the Parochial Schools of the Counties of Aberdeen ...

...produced, what change ought, from the nature of the case, to be made in the enunciation? 4. The angle ut the centre of a circle is double the angle at the circumference. Assuming that there is no limitation as to the magnitude of an angle, deduce from this proposition,... ## Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...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,... ## The elements of mechanism

Thomas Minchin Goodeve - 1870 - 294 pages
...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 c P... ## Four Phases of Morals: Socrates, Aristotle, Christianity, Utilitarianism

John Stuart Blackie - Christian ethics - 1871 - 432 pages
...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... ## Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...AB, is the centre. PROPOSITION XX. THEOREM. The angle (ACD) at the centre of a circle, is double of the angle at the circumference, when they have the same part of the circumference for their base. Firstly — Let either leg of the angle at the periphery pass through the centre ; and because in the... ## An Introduction to the Practical and Theoretical Study of Nautical Surveying

John Knox Laughton - Hydrographic surveying - 1872 - 222 pages
...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... ## Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 886 pages
...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,... ## Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...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... 