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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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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 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. Lot ABC be a circle, and BEC an angle nt the centre, and BAC an angle at the circumference, which...
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Primer of geometry

Francis Cuthbertson (geometer.) - 1876
...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 upon AB at the centre, and...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 páginas
...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 described touching...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 349 páginas
...extended, as we now proceed to shew. PROPOSITION C. THEOREM. The angle, not less than two right angles, at the centre of a circle is double of the angle at the cvrcumference, subtended by the same arc. Fig. 1. Fig. 2. In the © ACBD, let the angles AOB (not less...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877
...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...that is, upon the same part of the circumference. 6. If two straight lines cut one another within a circle, the rectangle contained by the segments of...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 413 páginas
...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 a circle,...
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Civil Service of India: Open Competition for the Regulations, Examinations ...

1878 - 228 páginas
...section, is equal to the square on half the line. Find the greatest rectangle having a given perimeter. 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 part of the circumference. P is any point on the circumference...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...bisecting at right angles any straight line, taken within the circle. PROP. xxxvi. THEOREM. (E. 3. 20, 21). The angle at the centre of a circle is double of the angle at th» circumference standing upon the same arc, that is, upon tha same part of the circumference. And...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - 1878
...might be stated thus :—Every normal to a circle passes through the centre. PROPOSITION XX. THEOREM. The angle at the centre of a circle is double of the an<jle at the circumference, subtended by the same arc. Let ABC be a ©, 0 the centre, BC any arc,...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 282 páginas
...AKE, ABE are equal right-angled triangles; hence, AK is equal to AB. Proposition 16. Theorem.—The angle at the centre of a circle is double of the angle...that is, upon the same part of the circumference. Let ABC be a circle, BDC the angle at the centre, and BA C the angle at the circumference upon the...
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