| ...ol two unequal lines, 13 equal to the rectangle contained by their sum and difference. SECTION III. **The angle at the centre of a circle is double of the...that is, upon the same part of the circumference.** Is this proposition true, if the base bo greater than a semicircle? If so, why has Euclid omitted it... | |
| Francis James Jameson - 1851 - 116 páginas
...extremity of a diameter at right angles to it, each will be a tangent to the second circle. 1848. (A), **The angle at the centre of a circle is double of the...that is, upon the same part of the circumference,** (in. 20.) (E). If two straight lines AEB, CED, in a circle, intersect in E, the angles subtended by... | |
| 1851
...of a given circle, 3. Prove that the diameter of a circle is the greatest chord, .... 4. Prove that **the angle at the centre of a circle is double of the angle at the circumference, upon the same base,** .... 5. Explain how the height of an inaceessibl object may be determined, . 6. What are the five regular... | |
| Charles Astor Bristed - 1852
...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 4. **The angle at the centre of a circle is double of the...that is, upon the same part of the circumference.** 5. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than... | |
| Royal Military Academy, Woolwich - 1853
...centre; that is, the centre is in CA. Therefore, if a straight line, etc. QED PROPOSITION XX. THEOR. **The angle at the centre of a circle is double, of...that is, upon the same part of the circumference.** BOOK III. PROF. XX., XXI. First, let E, the centre of the circle, be within the angle BAC, and join... | |
| Euclides - 1853 - 146 páginas
...5. The centre of the circle is in CA. Therefore, if a straight line, &e. QEU PROP. XX. — THEOREM. **The angle at the centre of a circle is double of the...that is, upon the same part of the circumference.** Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
| University of Sydney - 1853
...the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 8. **The angle at the centre of a circle is double of the angle at the circumference upon the same base.** Prove this, and thence shew that the angle in a semi circle is a right angle. 9. Two circles intersect... | |
| Dugald Stewart - 1854
...different quantities, and the connexions which exist between different relations. When we demonstrate that **the angle at the centre of a circle is double of the angle at the circumference** on the same base, we ascertain a relation between two quantities. When we demonstrate that triangles... | |
| Dugald Stewart - 1854
...different quantities, and the connexions which exist between different relations. When we demonstrate that **the angle at the centre of a circle is double of the angle at the circumference** on the same base, we ascertain a relation between two quantities. When we demonstrate that triangles... | |
| John Hind - 1855 - 328 páginas
...centre of the circle circumscribing the triangle ABC, we have OA=OB= ОС = the radius R : then, since **the angle at the centre of a circle is double of the angle at the circumference upon the same base,** we have, from Article (77), REGULAR POLYGONS. From this, it appears that the sine of any angle of a... | |
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