 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...in the Proposition called by Simson the Twentieth of the Third Book, the object of -vhich is to show that the angle at the centre of a circle is double of the angle at the circumference. COR. 16. If evidence is demanded of the existence of magnitudes which, being added together to any... | |
 | John Martin Frederick Wright - Astronomy - 1833 - 332 pages
...given point, 2c the radius of the generating circle of the cycloid = — TRINITY COLLEGE, JUNE 1832. 1. THE angle at the centre of a circle is double of the angle at the circumference upon the same base. 'io .& rtr • 3x* — ifix — 12 2. Reduce the fraction ; to its lowest ^3 _... | |
 | Euclides - 1834 - 518 pages
...that is, the centre is in ('A. Therefore, if a straight line, &c. y. ED PROPOSITION XX. TnEOR. — The angle at the centre of a circle is double of the See N. angle at the circumference upon the same base, thai is, upon the same pit rt of the circumference.... | |
 | Mathematics - 1835 - 684 pages
...magnitudes between one and two, two and three, three and four, &c. quadrants. PROP. 14. (Euc.iii. 20.) The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference. Let А С В be any angle at... | |
 | John Playfair - Geometry - 1836 - 148 pages
...the centre ; that is, the centre is in CA. Therefore, if a straight line, &c. QED B PROP. XII. THEOR. The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference. Let ABC be a circle, and BEC... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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 angle at the circumference, upon the same base, that is, upon the same arc. arc BC for their base ; the angle BDC is double of... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...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 angle at the circumference, upon the same base, that is, upon the same part of the circumference. Steps of the Demonstration to... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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 angle at the circumference, upon the same base, that is, upon the same part of the circumference. In the circle ABC, let BEC be... | |
 | Euclides - 1840 - 82 pages
...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 - Geometry - 1841 - 378 pages
...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... | |
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The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference. 
