 | John Playfair - Geometry - 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... | |
 | 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 angle at the circumference, upon the same base, that is, upon the same part of the circumference. EUCLID. BOOKS I. II. III.—... | |
 | 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 angle at the circumference upon the same base ; that is, upon the same part of the circumference. Let ABC (Fig. 47) be a circle,... | |
 | Peter Nicholson - Cabinetwork - 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... | |
 | John Playfair - Euclid's Elements - 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 angle at the circumference upon the same base, that is, upon the same part of the circumference. 9. From a given circle to cut... | |
 | 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 angle at the circumference upon the same base, that is upon the same part of the circumference. BOOK IV. 3. PROP. 11 — To inscribe... | |
 | 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... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 694 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 angle at the circumference upon the same base, that is, upon the same part of the circumference. 12. PROP. XXXI. — In a circle,... | |
 | 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 angle at the circumference upon the same base, that is, upon the same part of the circumference. 12. PROP. XXXI. — In a circle,... | |
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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. 
