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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.
A Treatise on Surveying, Containing the Theory and Practice: To which is ... - Página 43
por John Gummere - 1814 - 346 páginas
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The Elements of Plane and Solid Geometry

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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

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...
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Elements of geometry, containing the first two (third and fourth ..., Parte2

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...
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Euclid's Elements of Geometry

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...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

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...
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The Elements of Euclid, containing the first six books, with a selection of ...

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...
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Pure mathematics, Volumen1

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...
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Recent military, naval, and civil service examination papers in mathematics ...

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...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

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...
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Euclidian Geometry

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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