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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. "
The Projection and Calculation of the Sphere for Young Sea Officers Being a ... - Page 21
by S. M. Saxby - 1861 - 112 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...straight line, &c. QED B PROP. XX. THEOR. a 5 1. b 32. 1. 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 ABC be a circle, and BDC an angle at the centre, and BAG an angle at the circumference, which have...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...the centre is in CA. ED PROP. XX. THEOR. s«« N. 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. B a 5.1. b33. Let ABC be a circle, and BEC an angle at the centre, and Book III. BAC an angle at the...
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 398 pages
...the internal and opposite angles A and C. Fig. 3710. 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 : thus the angle EEC is double of the angle BAG. Fig- 38. i • 11. The angles in the same segment...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...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 is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, Bo°* mand BAC an angle at the circumference,...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...the circle shall be in that line. Prop. XX. Theor. 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. Prop. XXI. Theor. The angle» in the same segment of a circle are equal lo one another. Prop. XXII....
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...a straight line, &c. Q, E. D, -- PROP. XX. THEOR. 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 ABC be a circle, and BDC an angle at the centre, and BAC an angle at the circumference, which have...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...if a straight line, &c. QED PROP. XX. THEOR. See N. 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 ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...and four, &c. quadrants. PROP. 14. (Eue. iii. 20.) The a?igle 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 А С В be any angle at the centre С oí the circle A B'D, and let ADB be _D 86 GEOMETRY. an...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...; that is, the centre is in C A. Therefore, " if a straight line" &c. QED PROP. XX. THEOR. S«e N. The angle at the centre of a circle is double the...that is, upon the same part of the circumference. B a 5. 1. b 32. 1. Let ABC be a circle, and BEC an angle at the centre, Book in. and BAC an angle at...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...the centre ; that is, the centre is in C A. Therefore, " if a straight line" &c. QED PROP. XX. THEOR. The angle at the centre of a circle is double the...that is, upon the same part of the circumference. a 5. 1. . l. Let ABC be a circle, and BEC an angle at the centre, Book III. and BAC an angle at the...
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