Elements of Plane Geometry
Elements of Plane Geometry
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In our eReader you can find the full English version of the book. Read Elements of Plane Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Plane Geometry
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A straight line cannot cut a circumference in more than two points. Q. E. D.
8* 90 ELEMENTS OF PLANE GEOMETRY.
THEOREM IV.
186. In equal circles, or in the same circle, equal angles at the centre intercept equal arcs.
Let and P be the centres of the equal Os ABC and DEF, and let Z_ a = /- b.
I) To prove that arc AB = arc DE.
Place the OABC on the ODEF so that Z_ a coincides with Z_ b.
OA = OB = PD = PE; (182) A falls on D, and B falls on E; ABO = DEP, (14) and arc AB = arc D JE. Q. E. D.
187. C...OR. J?i equal circles, or in the same circle, equal arcs subtend equal angles at the centre.
ELEMENTS OF PLANE GEOMETRY.
91 THEOREM V.
188. In equal circles, or in the same circle, equal arcs are subtended by equal chords.
In the equal Os ABE and CDF, let arc AB = arc CD.
To prove that chord AB = chord CD.
Draw the radii OA, OB, PC, PD. OA = PC, OB = PD, and Z. A = /- b ; and chord AB chord CD.
(182) (182) (187) (83) Q. E. D.
189. COR. In equal circles, or in the same circle, equal chords subtend equal arcs.
What to read after Elements of Plane Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Franklin Ibach to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
A straight line cannot cut a circumference in more than two points. Q. E. D.
8* 90 ELEMENTS OF PLANE GEOMETRY.
THEOREM IV.
186. In equal circles, or in the same circle, equal angles at the centre intercept equal arcs.
Let and P be the centres of the equal Os ABC and DEF, and let Z_ a = /- b.
I) To prove that arc AB = arc DE.
Place the OABC on the ODEF so that Z_ a coincides with Z_ b.
OA = OB = PD = PE; (182) A falls on D, and B falls on E; ABO = DEP, (14) and arc AB = arc D JE. Q. E. D.
187. C...OR. J?i equal circles, or in the same circle, equal arcs subtend equal angles at the centre.
ELEMENTS OF PLANE GEOMETRY.
91 THEOREM V.
188. In equal circles, or in the same circle, equal arcs are subtended by equal chords.
In the equal Os ABE and CDF, let arc AB = arc CD.
To prove that chord AB = chord CD.
Draw the radii OA, OB, PC, PD. OA = PC, OB = PD, and Z. A = /- b ; and chord AB chord CD.
(182) (182) (187) (83) Q. E. D.
189. COR. In equal circles, or in the same circle, equal chords subtend equal arcs.
What to read after Elements of Plane Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Franklin Ibach to read onlineMoreLess
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