| Robert Potts - 1868 - 434 pages
...the remaining angle BA C. .. Therefore the angle at the center, &c. QED PROPOSITION XXI. THEOREM. The angles in the same segment of a circle are equal to one another. Let AB CD be a circle, , and BAD, BED angles in the same segment BAED. ' Then the angles BAD, BED shall... | |
| Edinburgh univ - 1868 - 334 pages
...contained by the whole, and one of the parts, may be equal to the square of the other part. 5. The angles in the same segment of a circle are equal to one another. 6. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting... | |
| James Maurice Wilson - Geometry - 1868 - 150 pages
...arc of a circle is half of the angle subtended by the same arc at the centre . . . . . . 11 COR. 1. Angles in the same segment of a circle are equal to one another . . . . . . . . . .12 COR. i. If a circle is divided into any two segments by a chord, the angles in... | |
| Great Britain. Education Department. Department of Science and Art - 1869 - 98 pages
...and triangles upon the same base and between the same parallels are equal to one another. (10.) 23 5. Angles in the same segment of a circle are equal to one another. *6. Divide a" — SaV + 3aV — a6 by a3 — 3a?x + Sax* — ar>. (10.) 7. Solve the equations : —... | |
| FREDERICK W. SIMMS - 1870 - 174 pages
...as compared with its extent, and is deduced from the well-known theorem, that all angles contained in the same segment of a circle are equal to one another.* The method is as follows :— Place a theodolite at B and another at 0, the two ter* Euclid, Book III,... | |
| Frederick Walter Simms - Leveling - 1870 - 220 pages
...as compared with its extent, and is deduced from the well-known theorem, that all angles contained in the same segment of a circle are e'qual to one another.* The method is as follows : — Place a theodolite at B and another at C, the two terminations of the... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...one, and only one, circumference can be drawn (Bk. II. Prop. 5, Cor.) ; let this be BPC. Because the angles in the same segment of a circle are equal to one another, if any point Q, different from P, be taken in the circumference BPC, the angle BQC will be equal to... | |
| John Fry Heather - Drawing instruments - 1871 - 236 pages
...may be accomplished without travelling beyond the limits of the drawing board. By Euclid iii. 36, the angles in the same segment of a circle are equal to one another, and the property demonstrated in this theorem has already been applied in the construction of the centrolinead,... | |
| Royal United Services Institute for Defence Studies - Military art and science - 1872 - 742 pages
...circumference upon the same luxe, that in, upon tha same part of the circumference. The 21st proves that the angles in the same segment of a circle are equal to one another. The 22nd proves that the opposite angles of any quadrilateral figure inscribed in a circle are together... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...lines drawn from any point in the arc to the extremities of the chord. PROPOSITION XXI. THEOREM. The angles in the same segment of a circle are equal to one another. Pig.I. Let BAG, BDC be angles in the same segment BADC. Then must L BAC= L BDC. First, when segment... | |
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