 | John Wright (Mathematician) - Perspective - 1772 - 298 pages
...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.... | |
 | Society for the diffusion of useful knowledge - 1841 - 522 pages
...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... | |
 | 1841 - 524 pages
...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... | |
 | Euclides - 1860 - 288 pages
...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... | |
 | Charles Knight - Encyclopedias and dictionaries - 1868 - 528 pages
...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... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...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... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...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)... | |
 | Thomas Smith (D.D.) - Euclid's Elements - 1902 - 244 pages
...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,... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...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... | |
 | Sir Thomas Little Heath - Mathematics - 1921 - 474 pages
...Peletarius (Pettier), Vieta, Galilei and Wallis. We now come to propositions about segments. 20 proves that the angle at the centre is double of the angle at the circumference, and 21 that the angles in the same segment are all equal, which leads to the property of the quadrilateral... | |
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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. 
