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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 schoolmaster: essays on practical education, selected from the works of ...

Schoolmaster - 1836 - 924 páginas
...of A and B is double of the sum or difference of C and D. It can thence be immediately proved that the angle at the centre of a circle is double of the angle at the circumference, and that all the angles in the same segment are equal. These we suppose to be also known facts, our...
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The Schoolmaster: Essays on Practical Education, Selected from the ..., Volumen1

1836 - 502 páginas
...of A and B is double of the sum or difference of C and D. It can thence be immediately proved that the angle at the centre of a circle is double of the angle at the circumference, and that all the angles in the same segment are equal. These we suppose to be also known facts, our...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...touching line, the centre of the circle is in that line. XX. The angle at the centre of a circle is double the angle at the circumference, upon the same base, that is, upon the same point of the circumference. XXI. The angles in the same segment of a circle are equal to one another....
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 112 páginas
...supposition is false, and .'. F is not the centre, 3. that the centre is in AC. PROPOSITION XX. Theorem. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Steps of the Demonstration to Case T.st, In which the centre E is within Z BAC. 1. Prove that Z EAB...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 410 páginas
...CA, is the centre ; that is, the centre is in CA. Therefore, if a straight line, &c. PROP. XX. THEOR. THE angle at the centre of a circle is double of the...that is, upon the same part of the circumference. In the circle ABC, let BEC be an angle at the centre, and BAC an angle at the circumference, which...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...the point of contact — if a line fulfil two, it also fulfils the third. PROPOSITION XX. THEOREM. The angle at the centre of a circle is double of the...circumference, upon the same base, that is, upon the same arc. arc BC for their base ; the angle BDC is double of the angle BAG. First, let D, the centre of...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 páginas
...of contact perpendicular to the tangent, passes through the centre of the circle. PROP. XX. THEOR. The angle at the centre of a circle, is double of the angle at the circumference, standing on the same arch. PROP. XXI. THEOR. All angles in the same segment of a circle are equal to...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 páginas
...is the centre; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR, The angle at the centre of a circle is double of the...angle at the circumference, upon the same base, that in, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and...
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Transactions of the Royal Scottish Society of Arts, Volumen4

Royal Scottish Society of Arts - 1856 - 862 páginas
...Prop. XX., Book III., Euclid, it is demonstrated that the angle at. the centre of a circle is double the angle at the circumference upon the same base that is upon the same part of the circumference. Let ABCDEF be a circular frame revolving on its centre at G, and let F be a point on the circumference...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...is the centre; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR, 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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