 | 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... | |
 | 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.... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...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,... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...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,... | |
 | Encyclopedias and dictionaries - 1816 - 764 pages
...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... | |
 | Euclides - 1821 - 294 pages
...without the line at right angles to the tangent, can be tbe centre of that «rcle. PROP. 20, THEOR. The angle at the centre of a circle is double the angle at the circumference, when, they have the same part of the circumference for their base. 1. Let one side of the angle at the circumference... | |
 | Charles Hutton - Mathematics - 1822 - 616 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,... | |
 | Ferdinand Rudolph Hassler - Geometry - 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... | |
 | 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 angle at the circumference upon the same base, that is, upon the same part of the circumference. B a 5. 1. b 32. 1. Let ABC be... | |
 | 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 angle at the circumference upon the same base, that is, upon the same part of the circumference. a 5. 1. . l. Let ABC be a circle,... | |
| |
The angle at the centre of a circle is double the angle at the circumference on the same arc. 
