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" The angles in the same segment of a circle are equal to one another. "
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... - Page 81
by Euclid, Robert Simson - 1829 - 516 pages
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Journal of the Royal United Service Institution, Volume 16, Issues 67-69

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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

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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The Acting Teacher's and Student's in Training Guide and Text Book for ...

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...
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A Descriptive Treatise on Mathematical Instruments: Their Construction, Uses ...

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...
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Introduction to quaternions, by P. Kelland and P.G. Tait

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. — S Up, shews that the angle in...
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Pure mathematics, Volume 1

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....
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The Elements of Euclid, containing the first six books, with a selection of ...

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...
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Euclidian Geometry

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...
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

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...
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The Madras University Calendar, Volume 1

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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