 | 1850 - 806 pagina’s
...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 - 1807 - 476 pagina’s
...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 - 1811 - 406 pagina’s
...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,... | |
 | Peter Fleming - 1815 - 250 pagina’s
...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... | |
 | Charles Hutton - 1816 - 610 pagina’s
...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,... | |
 | 1816 - 764 pagina’s
...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... | |
 | Charles Hutton - 1822 - 616 pagina’s
...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,... | |
 | Euclid, Dionysius Lardner - 1828 - 542 pagina’s
...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... | |
 | Ferdinand Rudolph Hassler - 1828 - 180 pagina’s
...-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 - 1833 - 216 pagina’s
...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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The angle at the centre of a circle is double the angle at the circumference on the same arc. 
