...angles BAC, BEG in it, are equal, by the first case. For the same reason, because the segment CAED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED. [Axiom 2. Wherefore, the angles in the same segment &c. QED PBOPOSITION 22. THEOREM. TlM opposite angles...

...rectangle contained by the sum and difference of two lines is equal to the difference of their squares. 3. The opposite angles of any quadrilateral figure, inscribed...a circle, are together equal to two right angles. ABC is an isosceles triangle, A being the vertex. In AB a point D is taken and in AC a point E, so...

...rectangle contained by the whole and one of the parts may be equal to the square on the other part. 3. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 4. To describe a circle about a given square. 5. If the vertical angle of a triangle be bisected by...

...double of the square on half the line and of the square on the line between the points of section. 5. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Prove that the converse proposition is also true. If in any quadrilateral the diagonals are equal to...

...Therefore, squares on AC and BD = squares on BA, AD, AD, and DC, ie, on BA, AD, DC, and CB. SECTION IV. — The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Show that if two of the adjacent angles are right angles, the figure is a square, but that if two of...

...whole and one of the parts may be equal to the square on the other part. 2. Euclid III, IV, VI. 8. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 9. Describe an isosceles triangle, having each of the angles at the base double of the third angle....

...any point, the straight line which joins their centres shall pass through the point of contact. 11. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 12. Describe a circle about a given triangle. 13. Enunciate those geometrical definitions which are...

...shall cut it at right angles ; and conversely, if it cut it at right angles, it shall bisect it. 8. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 9. From a given circle to cut off a segment which shall contain an angle equal to a given rectilineal...

...equal to three times the square on the radius of a circle which passes through its angular points. 2. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Show that if two of the adjacent angles are right angles, the figure is a square, but that if two of...

...described upon the other two sides of it, the angle contained by these two sides is a right angle. 3. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 4>. Define the terms figure, polygon, rectangle, circle inscribed in a rectilineal figure, rectilineal...