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The angle at the centre of a circle is double the angle at the circumference on the same arc.
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 130
by Euclides - 1833
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## The Eclectic review. vol. 1-New [8th]

1850 - 806 pages
...similar to those acts by which, knowing the previous propositions of Euclid, he might be assured that the angle at the centre of a circle is double the angle at the circumference, both angles standing on the same arc. On the contrary, our author would entirely exclude mathematical...
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## A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807 - 476 pages
...must be equal. Coral. Hence equal chords in a circle, subtend equal anglei at the circumference. 71. The angle at the centre of a circle is double the angle at the circumference when both of them stand on the same arc. Let G4\C be an angle at the centre, and GPA an angle at the circumference....
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## A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...the arc AEB ; and thus, having equal measures, they are equal to each other (ax. 11). THEOREM LI. An Angle at the Centre of a Circle is Double the Angle at the Circumference, when both stand on the Same Arc. Let c be an angle at the centre c, and D an angle at the circumference,...
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## A System of Land Surveying and Levelling: Wherein is Demonstrated ..., Volume 1

Peter Fleming - Surveying - 1815 - 242 pages
...equal to the opposite and inward angle, 4. The angles at the base of an isoceles triangle are equal, 5. The angle at the centre of a circle, is double the angle at the circumference, when standing upon the same arc of that circumference, ..---_ 6. The three angles of a triangle are equal...
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## A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well ...

Charles Hutton - Mathematics - 1816
...the arc AFB ; and thus, having equal measures, they are equal to each other (ax. 11). THEOREM LI. AN Angle at the Centre of a Circle is Double the Angle at the Circumference, when both stand on the Same Arc. Let c be an angle at the centre c, and D an angle at the circumference,...
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## Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 10

...perpendicular to a tangent at the point of contact, that line paffes through the centre. THEOR. XXf.yfif.j?. An angle at the centre of a circle is double the angle at the circumference •which Hands upon the fame arch. Let ACB he the angleat the centre of a circle and ADB an angle at...
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## A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...the arc AEB ; and thus, having equal measures, they are equal to each other («. 11). THEOREM Lt AN Angle at the Centre of a Circle is double the Angle at the Circumference, when both stand on the Same Arc. Let c be an angle at the centre c, and D an angle at the circumference,...
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## The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...impossible. PROPOSITION XX. (355) The angle (ACD) at the centre of a circle, is double the angle (ABD) at the circumference, when they have the same part of the circumference for their base. 1°. Let the centre be on AB a side of the angle ABD at the circumference. Because in the triangle DCB the sides...
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## Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Electronic book - 1828 - 180 pages
...-angle at the centre, and to these equal angles equal arcs will correspond. § 49. THEOREM. The an^le at the centre of a circle is double the angle at the circumference, that is subtended by the same chord or arc. APPLIC. In the circles ADBE, (fig. 53 and 54,) let the...
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## The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...PROP. XX. THEOR. Fig. 27,23, The angle (ACD) at the centre of a circle is double °f th0 angle (ABD) at the circumference, when they have the same part of the circumference for their base. e N Fig. 27. (1) Prop. 5. B. 1. (2) Prop. 32. B. 1. Fig. 28. 1. Let one leg of the angle at the circumference...
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