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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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Papers for the schoolmaster, Volúmenes1-6

...ol two unequal lines, 13 equal to the rectangle contained by their sum and difference. SECTION III. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Is this proposition true, if the base bo greater than a semicircle? If so, why has Euclid omitted it...
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The Principles of the Solution of the Senate-house 'riders,' Exemplified by ...

Francis James Jameson - 1851 - 116 páginas
...extremity of a diameter at right angles to it, each will be a tangent to the second circle. 1848. (A), The angle at the centre of a circle is double of the...that is, upon the same part of the circumference, (in. 20.) (E). If two straight lines AEB, CED, in a circle, intersect in E, the angles subtended by...
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Annual Report of the Commissioners ...

1851
...of a given circle, 3. Prove that the diameter of a circle is the greatest chord, .... 4. Prove that the angle at the centre of a circle is double of the angle at the circumference, upon the same base, .... 5. Explain how the height of an inaceessibl object may be determined, . 6. What are the five regular...
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Five Years in an English University, Volumen2

Charles Astor Bristed - 1852
...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. 5. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...centre; that is, the centre is in CA. Therefore, if a straight line, etc. QED PROPOSITION XX. THEOR. The angle at the centre of a circle is double, of...that is, upon the same part of the circumference. BOOK III. PROF. XX., XXI. First, let E, the centre of the circle, be within the angle BAC, and join...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 páginas
...5. The centre of the circle is in CA. Therefore, if a straight line, &e. QEU PROP. XX. — THEOREM. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have...
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The Sydney University Calendar

University of Sydney - 1853
...the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 8. The angle at the centre of a circle is double of the angle at the circumference upon the same base. Prove this, and thence shew that the angle in a semi circle is a right angle. 9. Two circles intersect...
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The Collected Works of Dugald Stewart: Elements of the philosophy of the ...

Dugald Stewart - 1854
...different quantities, and the connexions which exist between different relations. When we demonstrate that the angle at the centre of a circle is double of the angle at the circumference on the same base, we ascertain a relation between two quantities. When we demonstrate that triangles...
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The Collected Works of Dugald Stewart, Esq., F.R.SS., ...: Elements of the ...

Dugald Stewart - 1854
...different quantities, and the connexions which exist between different relations. When we demonstrate that the angle at the centre of a circle is double of the angle at the circumference on the same base, we ascertain a relation between two quantities. When we demonstrate that triangles...
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The Elements of Plane and Spherical Trigonometry

John Hind - 1855 - 328 páginas
...centre of the circle circumscribing the triangle ABC, we have OA=OB= ОС = the radius R : then, since the angle at the centre of a circle is double of the angle at the circumference upon the same base, we have, from Article (77), REGULAR POLYGONS. From this, it appears that the sine of any angle of a...
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