 | Henry Major - 1873 - 588 Seiten
...it may be shewn that no other point out of CA is the centre ; therefore the centre is in CA. 1TX — The angle at the centre of a circle is double of the angle at the circumference on the same base, that is, on the same arc. Let ABC be a circle, and BEC an angle at... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 Seiten
...converse of each of the above Propositions is evidently also true. PROP. XII.— THEOREM. (Euc. I. 20.) The angle at the centre of a circle is double of the angle at the circumference on the same base, that is, on the same arc. Let AOB be an angle at the centre, and APB... | |
 | Euclides - 1874 - 342 Seiten
...centre of the circle is in CA. Therefore, if a straight line, &c. QED PROPOSITION 20. — 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. Let A BC be a circle,... | |
 | Edward Atkins - 1874 - 428 Seiten
...therefore the centre is in CA. Therefore, if a straight line, &c. QED Proposition 20. — 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. Let ABC be a circle, and BEG an angle... | |
 | Braithwaite Arnett - 1874 - 130 Seiten
...straight line which joins their centres, being produced, shall pass through the point of contact. 4. The angle at the centre of a circle is double of the angle at the circumference on the same base, that is, on the same arc. AB and CD are two chords in a circle which... | |
 | Francis Cuthbertson - 1874 - 400 Seiten
...off. An angle is said to stand upon the circumference intercepted between its arms. PROPOSITION XIII. The angle at the centre of a circle is double of the angfe at the circumference upon the same arc. Let AB be an arc of a © of which C is the centre, ACB... | |
 | Francis Cuthbertson (geometer.) - 1876 - 102 Seiten
...QEF ANGLES IN CIRCLES. DEFINITION. An arc of a circle is a part of the circumference. PROPOSITION V. The angle at the centre of a circle is double of the angle at the circumference upon the same arc. Let AB be an arc of a circle of which C is the centre, ACB the angle... | |
 | Robert Potts - 1876 - 446 Seiten
...drawn through it, the tangents to the circles from any point in this perpendicular may be equal. >. The angle at the centre of a circle is double of the angle at the circumference npon the same base, that is, npon the same part of the circumference. If n circle be... | |
 | Edward Atkins - 1876 - 130 Seiten
...therefore the centre is in CA. Therefore, if a straight line, &c. QED Proposition 20. — 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. Lot ABC be a circle, and BEC an angle... | |
 | Samuel H. Winter - 1877 - 452 Seiten
...is equal to the square on the straight line which is made up of the half and the part produced. 5. The angle at the centre of a circle is double of the angle at the circumference on the same base that is on the same arc. 6. If two straight lines cut one another within... | |
| |
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. 
