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PROPOSITION 20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base.
A new supplement to Euclid's Elements of geometry, by the author of 'A new ... - Pagina 57
door Joseph Denison - 1840 - 84 pagina’s
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## Elements of Trigonometry, Plane and Spherical: With The Principles of ...

John Wright (Mathematician) - 1772 - 251 pagina’s
...AD, cutting CA in 10, 20, 30, &c. CA ihall be divided into a line of half tangents. Becaufe [20. 3.] the angle at the centre is double of the angle at the circumference, fo the lines C1o, C2o, Cjo, &c. on CA, are the tangents of 5, 10, 15, degrees of a circle of this radius....
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## The penny cyclopędia [ed. by G. Long]., Volume 20

...centre is double of that at the circumference.' It is true thai his proposition is, ' In a circle, the angle at the centre is double of the angle at the circumference when they have the mine circumference for a base:' and some may think that the words in italics exclude...
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## The Penny Cyclopaedia of the Society for the Diffussion of Useful ..., Volume 20

1841
...centre is double of that at the circumference.' It is true that his proposition is, ' In a circle, the angle at the centre is double of the angle at the circumference when they have the same circumference fnr a base .•' and some may think that the words in italics...
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## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...away the common angle DAO, and there remains the angle ODB equal to twice the angle CAO ; that is, the angle at the centre is double of the angle at the circumference. PROPOSITION (D). THEOREM. [To be substituted for III. 35 of the Element*.] ft . sIf two chords in a...
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## Arts and Sciences: Or, Fourth Division of "The English Encyclopedia", Volume 7

Charles Knight - 1868
...centre is double of that at the circumference." It is true that his proposition is, " In a circle, the angle at the centre is double of the angle at the circumference wh(n they hare the tame circumference for a late:" and some may think that the words in italics exclude...
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## Modern Methods in Elementary Geometry

E. M. Reynolds - 1868 - 112 pagina’s
...are equal; also a line which is nearer to the centre is greater than one more remote. THEOREM XIIL The angle at the centre is double of the angle at the circumference which stands upon the same arc. Let A OB, A CB be angles at the centre and at the circumference which...
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## An Elementary Course of Plane Geometry

Richard Wormell - 1870 - 16 pagina’s
...circumference, is termed an inscribed angle ; it is said to stand upon the arc intercepted by its sides. An angle at the centre is double of the angle at the circumference on the same arc. 206. There are three cases to consider, according as the centre of the circle is (i)...
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## Euclid, His Life and System

Thomas Smith (D.D.) - 1902 - 227 pagina’s
...his propositions is inconsistent with one of his definitions. The proposition III. 20 is that " an angle at the centre is double of the angle at the circumference standing on the same arc." Now it is afterwards 1 Thus, if a represent 4 inches and 6 represent 5 inches,...
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## Books 3-9

Euclid - 1908
...point at right angles to the line of centres is a tangent to both circles. PROPOSITION 20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base. Let ABC be a circle, let the angle EEC be an angle...
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## The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association, Mathematical Association of America - 2003 - 541 pagina’s
...Prop. 14: To construct a square equal to a given rectilineal figure. Book III Prop. 20: In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base. Prop. 21 : In a circle the angles in the same...
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