 | Royal United Services Institute for Defence Studies - 1872 - 742 sider
...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 - 1872 - 376 sider
...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 - 1873 - 588 sider
...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 - 1873 - 288 sider
...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 sider
...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 sider
...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 sider
...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 - 1874 - 400 sider
...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 sider
...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 sider
...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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The angles in the same segment of a circle are equal to one another. 
