| Schoolmaster - 1836 - 924 páginas
...of A and B is double of the sum or difference of C and D. It can thence be immediately proved that **the angle at the centre of a circle is double of the angle at the circumference,** and that all the angles in the same segment are equal. These we suppose to be also known facts, our... | |
| 1836 - 502 páginas
...of A and B is double of the sum or difference of C and D. It can thence be immediately proved that **the angle at the centre of a circle is double of the angle at the circumference,** and that all the angles in the same segment are equal. These we suppose to be also known facts, our... | |
| 1836 - 472 páginas
...touching line, the centre of the circle is in that line. XX. The angle at the centre of a circle is double **the angle at the circumference, upon the same base, that is, upon the same** point of the circumference. XXI. The angles in the same segment of a circle are equal to one another.... | |
| Euclides - 1837 - 112 páginas
...supposition is false, and .'. F is not the centre, 3. that the centre is in AC. PROPOSITION XX. Theorem. **The angle at the centre of a circle is double of the...that is, upon the same part of the circumference.** Steps of the Demonstration to Case T.st, In which the centre E is within Z BAC. 1. Prove that Z EAB... | |
| Euclid - 1837 - 410 páginas
...CA, is the centre ; that is, the centre is in CA. Therefore, if a straight line, &c. PROP. XX. THEOR. **THE angle at the centre of a circle is double of the...that is, upon the same part of the circumference.** In the circle ABC, let BEC be an angle at the centre, and BAC an angle at the circumference, which... | |
| Andrew Bell - 1837 - 240 páginas
...the point of contact — if a line fulfil two, it also fulfils the third. PROPOSITION XX. THEOREM. **The angle at the centre of a circle is double of the...circumference, upon the same base, that is, upon the same** arc. arc BC for their base ; the angle BDC is double of the angle BAG. First, let D, the centre of... | |
| Euclides - 1840 - 82 páginas
...of contact perpendicular to the tangent, passes through the centre of the circle. PROP. XX. THEOR. **The angle at the centre of a circle, is double of the angle at the circumference,** standing on the same arch. PROP. XXI. THEOR. All angles in the same segment of a circle are equal to... | |
| Euclides - 1841 - 378 páginas
...is the centre; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR, **The angle at the centre of a circle is double of the...angle at the circumference, upon the same base, that** in, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and... | |
| Royal Scottish Society of Arts - 1856 - 862 páginas
...Prop. XX., Book III., Euclid, it is demonstrated that the angle at. the centre of a circle is double **the angle at the circumference upon the same base that is upon the same part of the circumference.** Let ABCDEF be a circular frame revolving on its centre at G, and let F be a point on the circumference... | |
| Euclides - 1842
...is the centre; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR, **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... | |
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