| 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... | |
| 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,... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| United States Naval Academy - 1874 - 888 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,... | |
| 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... | |
| Āryabhaṭa - 1878 - 100 pages
...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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