| 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... | |
| Henry Major - Student teachers - 1873 - 588 pages
...is double of the remaining angle BAC. XXI. — The angles in the same segment of a circle are equal. **Let ABCD be a circle, and BAD, BED, angles in the...BED are equal to one another. Take F the centre of** ABCD. First let the segment BAED be greater than a semicircle. Join BF, DF. Because the angle BFD is... | |
| William Ford Stanley - Drawing instruments - 1873 - 288 pages
...oftenrepeated thirty-first proposition of the third book of " Euclid's Elements of Geometry : " " The **angles in the same segment of a circle are equal to one another."** In practice this is well understood by the intelligent mechanic, who, to draw his arc through three... | |
| Philip Kelland - 1873 - 248 pages
...whilst pl varies, the right-hand side of this equation is constant, and the equation shews that the **angles in the same segment of a circle are equal to one another.** Further, the form of the right-hand side of the equation, viz. — Sß Up, shews that the angle in... | |
| Edward Atkins - 1874 - 428 pages
...remaining angle BAC. Therefore, the angle at the centre, &c. QED Proposition 21.— Theorem. f Tlie **angles in the same segment of a, circle are equal...angles in the same segment BAED. The angles BAD, BED** shall be equal to one another. CASE I. — First, let the segment BAED be greater than a semicircle.... | |
| Euclides - 1874 - 342 pages
...the remaining angle BAC. Therefore the angle at the centre, &c. QED PROPOSITION 21. — Theorem. The **angles in the same segment of a circle are equal to...circle, and BAD, BED angles in the same segment BAED.** Then the angles BAD, BED shall be equal to one another. First. Let the segment BAED be greater than... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...segment to the extremities- of the straight line which is the base of the segment. PROPOSITION XIV. The **angles in the same segment of a circle are equal to one another. Let** APB, AQB be angles in the same segment APQB. The L APB shall be = L AQB. i st. Let the segment be greater... | |
| Braithwaite Arnett - 1874 - 130 pages
...straight line which joins their centres, being produced, shall pass through the point of contact. 5. The **angles in the same segment of a circle are equal to one another.** Of all the triangles upon the same base, and having the same vertical angle, prove that the isosceles... | |
| University of Madras - 1874 - 502 pages
...point of contact. (a.) What subsequent proposition is assumed in this enunciation ? VIII. Prove that **angles in the same segment of a circle are equal to one another.** (a.) ABC is any chord of a circle whose centre is O, and meets the circle in A and C. Another circle^is... | |
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