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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. "
Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 73
by Euclides - 1842
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...case : for the same reason, because С bed is greater than a semicircle, the angles с a cL С ed, are equal : therefore the whole angle bad is equal to the whole angle bed. Wherefore the angles ia the same segment, &c. QED PROPOSITION XXII. — THEOREM. The opposite angles of any quadrilateral...
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Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...line thus produced and the part produced shall be equal to the square of the given straight line. 3. The opposite angles of any quadrilateral figure inscribed...a circle are to'gether equal to two right angles. If the opposite sides of the quadrilateral be produced to meet in P, Q, and about the triangles so...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 282 pages
...Euclid's figure, the rectangle contained by CF and FA is proved to be equal to the square on CA. 3. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. If the opposite sides of the quadrilateral be produced to meet in P, $, and about the triangles so...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...described upon the other two sides of it; the angle contained by these two sides is a right angle. 4. The opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles. ' 3. ABC is a triangle having a right angle at C. Points I) and E are taken in the base so that AD...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...СAD and СED are also equal, by the first case. Therefore the whole angle BAD is equal (I. Ax. 2) to the whole angle BED. Wherefore the angles in the same segment, &c. QED Corollary. — The vertices of any number of equal angles, whose legs all pass through the same two...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...semicircle, and the angles in it BAG, BEG are equal by the first case. For the same reason, because CBED is greater than a semicircle, the angles CAD, CED...therefore, the whole angle BAD is equal to the whole BED. LXL— EUCLID III. 22. The opposite angles of any quadrilateral figure inscribed in a circle are...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...equal angles stand upon equal circumferences whether they be at the centres or the circumferences. 11. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Two opposite sides of a quadrilateral figure are together equal to the other two and each of its angles...
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Manual of Method for the use of teachers in elementary schools

W F. Richards - Elementary school teaching - 1856 - 198 pages
...distant from the centre, and conversely those which are equally distant from the centre are equal. • 2. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 3. If two lines intersect each other either within or without a circle, and also intersect the circle,...
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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 390 pages
...Merchandise account." FRIDAY, Dec. 17, 1858. 9 to 12. II. 7. $ure Jilatl)etnatics. (HIGHER PAPER.) 1. THE opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. If segments of a circle be described with the same radius on the three sides of a triangle, shew that...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 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, are equal : therefore the whole angle BAD isequal to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION...
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