| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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