 | Braithwaite Arnett - 1874 - 130 pages
...the centre, it shall cut it at right angles ; and if it cut it at right angles it shall bisect it. 6. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. From the point A in the circumference of the circle APQB three chords AP, AQ, and AB are drawn so that... | |
 | University of Madras - 1874 - 502 pages
...line AB in C so that the rectangle contained by AC, CB may be twice the square on AC. II. Provp that the opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Also state and prove the converse of this proposition. III. Inscribe a circle in a given triangle.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...»nd the angles in it BA C, B EC are equal, by the first cas.tt> for the same reason, because CBED is greater than a semicircle, the angles CAD, CED,...the whole angle BAD is equal to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXII. THEOREM. The opposite... | |
 | Education Department,London - 1876 - 1010 pages
...В are tangents at A, B, and AD is a diameter. Shew that the angle AC В is twice the angle BAD. 3. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. The lines bisecting any angle of the inscribed quadrilateral and the opposite exterior angle meet in... | |
 | Edward Atkins - 1876 - 130 pages
...the angles BAC, BEC in it are equal by the first case. For the same reason, because the segment CBED is greater than a semicircle, the angles CAD, CED are equal. Therefore the whele angle BAD is equal to the whele angle BED (Ax, 2). Therefore, the angles in the same segment,... | |
 | D. Tierney - 1877 - 126 pages
...straight line which joins their centres being produced, shall pass through that point of contact. 7. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. From the point C, the straight lines CA and CB are drawn touching the circle PAB whose centre is O... | |
 | Āryabhaṭa - 1878 - 100 pages
...angles CAD and CED are also equal, by the first case. Therefore the whole angle BAD is equal (Ax. 2) to the whole angle BED. Wherefore the angles in the same segment, &c. QED PROP. xxxvii. THEOREM. (E. 3. '35). If two straight lines cut one another in a circle, the rectangle contained... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...semicircle; and the angles in it, BAC, BEC, are equal by the first case; for the same reason, because CBED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED. Corollary.—The angles in a circle standing on the same arc are equal to one another. Proposition... | |
 | Edward Harri Mathews - 1879 - 94 pages
...diagonals are parallel to the sides of the parallelogram, and equal to the difference between them. 2. The opposite angles of any quadrilateral figure inscribed...a circle are together equal to' two right angles. Two triangles are formed by lines drawn through the points A, B, C perpendicular to the lines AB, BC,... | |
 | University of Oxford - Education, Higher - 1879 - 584 pages
...circumference, that point is the centre of the circle. 9. Describe a circle about a given square. 10. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 2. EXAMINATION FOB CLASSICAL HONOURS. w I. THE FOUR GOSPELS. 1. Translate: — (l) Kai its rjv 8' av... | |
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CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED. 
