| Robert Simson - Trigonometry - 1835 - 513 pages
...CA, is the centre ; that is, the centre is in C A. Therefore, " if a straight line" &c. QED PROP. XX. **THEOR. 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. a 5. 1. . l. Let ABC be a circle,... | |
| Euclid - 1835 - 540 pages
...; that is, the centre is in C A. Therefore, " if a straight line" &c. QED PROP. XX. THEOR. S«e N. **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. B a 5. 1. b 32. 1. Let ABC be... | |
| Mathematics - 1836 - 472 pages
...straight line be drawn at right angles to the 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... | |
| Charles Reiner - Geometry - 1837 - 254 pages
...not equal to each other, and the lesser chord is farther from the centre than the greater chord. 11. **The angle at the centre of a circle is double the angle at the circumference,** upon the same arc. 12. At the circumference, an angle which stands upon a semi-circumference is a right... | |
| Royal Scottish Society of Arts - Industrial arts - 1856 - 860 pages
...apparatus I have termed a semi-revolving one. In 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... | |
| Euclides - 1846 - 272 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... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...Therefore, if a straight line, <fec. QED Recite (a) p. 18, 3 ; (4) def. 10, 1 ; (c)ax. 10; (d)ax.9. 20 Th. **The angle at the centre of a circle is double the angle at the circumference** upon the same arc. The angles AEB, BEC, AEC are central: The angles ADB, BDC, ADC are at the circumference,... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...upon the same arc, are equal to each other ; for each is measured by half the same arc. Cor. 2. An **angle at the centre of a circle is double the angle at the circumference, when** both stand on the same arc. For the angle at the centre is (B. lll, Def. 12) measured by the whole... | |
| Electronic journals - 1891 - 670 pages
...the angle be the ame ? Is GENERAL DRATSON acquainted with an obscure writer who long ago proved that **the angle at the centre of a circle is double the angle at the circumference** t But probably Euclid was a fossil geometer, as all who disagree with GENERAL. DRATSON are fossil astronomers.... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...subtended by the same arc, are equal to each other; for each is measured by half ihe same arc. Cor. 2. An **angle at the centre of a circle is double the angle at the circumference, when** both are subtended by the same arc. For the angle at the centre is (B. Ill, Def. 13,) measured by the... | |
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