Euclid's Elements of geometry, transl. To which are added, algebraic demonstrations to the second and fifth books Volume bks. 1-6 - Brossura

Euclides

Brossura

ISBN 10: 1130712273 ISBN 13: 9781130712278

Casa editrice: RareBooksClub.com, 2012

Riassunto

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1826 Excerpt: ...the centre, which stands on an arc equal to the sum or difference of the arcs intercepted between them, according as they meet within or without the circle. PROPOSITION XXL Theorem. In a circle the angles which are in the same segment are equal to one another. Let Abcde be a circle, and the angles Bad, Bed, in the same segment, Bacd. These angles are equal to one another. For find the centre of the circle Abcde, which let be F, and join Bf, Fd. Because the angle Bfd is at the centre, and the angle Bad at the circumference, also they have the same circumference Bcd for c their base, the angle Bfd" will be double of the angle 20. 3. Bad. For the same reason, the angle Bfd is double of the angle Bed. Wherefore the angle Bad will be equal to the angle Bed. If the angles Bad, Bed, are in a segment less than a semicircle, draw Ae, and all the angles of the triangle Abg will be equal to all the angles of the triangle Deg,15 and the angles Abe, Ade, b 32.1. are equal, as have been demonstrated, and the angles Agb,c Dge, are also equal, for they are vertically op-c 15.1. Eosite. Wherefore also the remaining angle Bag will e equal to the remaining angle Ged. Therefore in a circle, &c. Q. E. D. Deductions. 1. If from a given point within a circle, which is not the centre, right lines be drawn to the circumference, making with each other equal angles, the two, which are nearest to the diameter passing through the Part 1. G given point, shall cut off a greater circumference than the two, which are more remote. 2. Given the segments of the base of a triangle made by a perpendicular drawn from the vertex and the v.ertical angle to construct the triangle. PROPOSITION XXII. Theorem. The opposite angles of quadrilateral figures wkich are inscribed in a circle are eq...

Dettagli dell?edizione

• Editore: RareBooksClub.com
• Data di pubblicazione: 2012
• ISBN 10: 1130712273
• ISBN 13: 9781130712278
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 60