 | Henry William Watson - 1871 - 320 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 - 376 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 - 102 páginas
...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 - 284 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 - 588 páginas
...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 - 428 páginas
...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 - 130 páginas
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 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 - 400 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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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. 
