...propositions, has rendered it necessary that he should, in the succeeding proposition, demonstrate that " The angles in the same segment of a circle are equal to one another," a proposition which presented two cases requiring separate consideration. It was absolutely...

...lines (7T\ / 7T\ 0 ' , p = a sec 0 • 1 9 2/ l V 6) and the angle between them. 8. Prove analytically that the angles in the same segment of a circle are equal to each other. 9. Lp is a normal to a parabola at L the extremity of the latus rectum, meeting the...

...20 18 I 2. Inscribe an equilateral and equiangular hexagon in a given circle, i . > _ 8 1 3. Prove that the angles in the same segment of a circle are equal, ..... _ 7 8 4. Given two sides and the contained angle to resolve the triangle, ...... _ 7 4 5. Define...

...something to be proved, «s that triangles having the same base and altitude ore equal to each other, or that the angles In the same segment of a circle are equal. When something Is premised, or demonstrated, In order to render what follow» more easy, It Is termed...

...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...

...constant 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...

...obtuse, according as AD is greater than, equal to, or less than BD, the half of the base. 5. Prove that the angles in the same segment of a circle are equal to one another. BAG, BA'C are two angles in the same segment of a circle, and AP, A'P' are drawn cutting...

...produced lines in D and E : prove that the rectangle of BC, CD is equal to that of AC, CE. 8. Prove that the angles in the same segment of a circle are equal to one another. 9. Draw a tangent to a circle from any point without it. 10. If two straight lines...

...angles : and if it cut it at right angles it shall bisect it. 7" Define a segment of a circle, and prove that the angles in the same segment of a circle are equal to one another. OA, OR are two straight lines meeting in 0 ; a circle is drawn through 0 and a fixed...

...be interesting. The principle of its construction is based upon the 2ist prop., 3rd book of Euclid, that the angles in the same segment of a circle, are equal to one another. Two angles are taken by a sextant between a middle point and an object right and left...