 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...centre ; therefore the centre is in CA. Wherefore, 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 on the same base, that is, on the same arc. Let ABC\i& a circle, and BEC an angle... | |
 | Schools inquiry commission - Education - 1868 - 682 pages
...two numbers diminished by twice their product. Prove this both geometrically and algebraically. 20 5. 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. 10 G. The... | |
 | General Medical Council (Great Britain) - 1869 - 402 pages
...line. 2. Parallelograms upon equal bases and between the same parallels are equal to one another. 3. The angle at the centre of a circle is double of the angle at the circumference upon the same base. 4. Divide x? + 11 x 3 + x 2 - 12 x 4- 12 by x 3 - x + 1 :... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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... | |
 | Euclides - 1872 - 102 pages
...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... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...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... | |
 | Braithwaite Arnett - 1874 - 130 pages
...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... | |
 | Euclides - 1874 - 342 pages
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...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,... | |
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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 
