 | John Playfair - 1855 - 334 pages
...no other point which is not in CA, is the centre ; that is, the centre is in CA. B PROP. XX. THEOR The angle at the centre of a circle is double of the angle at the circumjerence, upon the same base, that is, upon the same part of the circumfer ence. Let ABC be a... | |
 | Euclides - 1856 - 168 pages
...therefore the square of EH is less than the square of EK, and the line EH than E K. LIX.— EUCLID III. 20. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC (Fig. 47) be a circle, BEC an angle at the centre, and BAC an angle at the circumference, having... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...line from a given point, either without or in the circumference, which shall touch a given circle. 11. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. EUCLID. BOOKS I. II. III.— (A.) For all Candidates for a BA Degree. 1. WHAT is meant by an axiom... | |
 | Peter Nicholson - 1856 - 518 pages
...to AB, which is impossible : therefore the angle ACB is equal to DCE. THEOREM 34. 91. An angle, ACB, at the centre of a circle, is double of the angle at the circumference, upon the same arc, AB. Draw DC, (fig. I,) and produce it to E. First, let the angle at the centre be within the angle... | |
 | John Playfair - 1856 - 346 pages
...that no other point which is not in CA, is the centre ; that is, the centre is in CA. PROP. XX. THEOR The angle at the centre of a circle is double of the angle at th» circumference, upon the same base, that is, upon the same part of the circumfer ence. Let ABC... | |
 | 1857 - 408 pages
...more than two equal straight lines to the circumference, that point is the centre of the circle. 8. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. 9. From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal... | |
 | 1858 - 398 pages
...which has the greater angle, shall be greater than the base of the other. BOOK III. 2. PROP. 20. — The angle at the centre of a circle is double of the...base, that is upon the same part of the circumference. BOOK IV. 3. PROP. 11 — To inscribe an equilateral and equiangular pentagon in a given circle. BOOK... | |
 | War office - 1858 - 578 pages
...amounts they respectively receive. Euclid. 1. Describe a square equal to a given rectilineal figure. 2. The angle at the centre of a circle is double of the angle at the circumference upon the same base. VOLUNTARY PORTION. 1. Define the sine of an angle ; trace the changes in the sign and magnitude of... | |
 | Great Britain. Parliament. House of Commons - 1858 - 694 pages
...another, which do not both pass through the centre, they do not bisect each other. 9. PROP. XX. — The angle at the centre of a circle is double of the angle at the circumference upon thai same base, that is, upon the same part of the circumference. 10. PROP. XXXVI. — If from any... | |
 | Joseph Charles Parkinson - 1860 - 154 pages
...equal straight lines to the circumference, that point is the centre of the circle. 11 . PROP. XX. — The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. 12. PROP. XXXI. — In a circle, the angle in a semicircle is a right angle; but the angle in a segment... | |
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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. 
