| Henry William Watson - 1871 - 285 páginas
...whatever, ie. whether greater or less than two right angles (Bk. II. Note, p. 74). Corollary 1. — Since **the angle at the centre of a circle is double of the angle at the circumference** subtended by the same arc, and since magnitudes have to one another the same ratio that their equimultiples... | |
| Euclides, James Hamblin Smith - 1872 - 349 páginas
...might be stated thus '.—Every normal to tvrcU passes through the centre. PROPOSITION "KX. THEOREM. **The angle at the centre of a circle is double of the angle at the circumference,** subtended by the same arc. • Let ABC be a © , O the centre, BCany arc, A any pt. in the Oce. Then... | |
| Euclides - 1872
...touch the less, the parts intercepted between the two circles are equal. PEOPOSITION XX. THEOREM. Tfte **angle at the centre of a circle is double of the angle at the circumference,** subtended by the same arc. Let ABC be a ©, O the centre, j .0(7 any arc, A any pt. in the Oce. Then... | |
| Euclid - 1872 - 261 páginas
...that no other point without the right line 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... | |
| Henry Major - 1873
...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 the centre, and... | |
| Euclides - 1874 - 342 páginas
...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...that is, upon the same part of the circumference.** Let A BC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which... | |
| Edward Atkins - 1874
...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...circumference, upon the same base, that is, upon the same** arc. Let ABC be a circle, and BEG an angle at the centre, and BAC an angle at the circumference, which... | |
| Braithwaite Arnett - 1874
...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 intersect when... | |
| Euclides - 1874 - 234 páginas
...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 an angle at... | |
| Francis Cuthbertson - 1874 - 349 páginas
...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... | |
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