Elementary Geometry Including Plane Solid And Spherical Geometry With Pract
Elementary Geometry Including Plane Solid And Spherical Geometry With Pract
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In our eReader you can find the full English version of the book. Read Elementary Geometry Including Plane Solid And Spherical Geometry With Pract 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 Elementary Geometry Including Plane Solid And Spherical Geometry With Pract
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To quickly assess the difficulty of the text, read a short excerpt:
— To inscribe a regular decagon in a circle, and hence a regular pentagon, and regular polygons of 20, 40, 80, etc. , sides.
Solution.
Let it be required to inscribe a regular decagon in the circle whose centre is and radius OA.
Divide the radius OA in extreme and mean ratio, as at (a).
Then is ac, the greater segment, the side of the in- scribed decagon, ABODE, etc.
To prove this, draw OA and OB, and taking CM = ° Fig. 215.
ac = AB, draw BM.
^^^ OM ~ MA ' ^y construction ; and, as OM = AB, we ...have 0A_ AB AB ~ MA * Hence, considering the antecedents as belonging to the triangle OAB, and the consequents to the triangle BAM, we observe that the two sides about the angle A, which is common to both triangles, are proportional ; hence the triangles are similar (373).
EXERCISES. 201 Therefore, ABM is isosceles, since OAB is, and angle BMA = A = OBA, and MB = BA = OM.
This makes 0MB also isosceles, and the angle = OBM. Again, the exterior angle BMA = + OBM = 20; hence, A (which equals BMA) = 20.
What to read after Elementary Geometry Including Plane Solid And Spherical Geometry With Pract?
You can find similar books in the "Read Also" column, or choose other free books by Edward Olney to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
— To inscribe a regular decagon in a circle, and hence a regular pentagon, and regular polygons of 20, 40, 80, etc. , sides.
Solution.
Let it be required to inscribe a regular decagon in the circle whose centre is and radius OA.
Divide the radius OA in extreme and mean ratio, as at (a).
Then is ac, the greater segment, the side of the in- scribed decagon, ABODE, etc.
To prove this, draw OA and OB, and taking CM = ° Fig. 215.
ac = AB, draw BM.
^^^ OM ~ MA ' ^y construction ; and, as OM = AB, we ...have 0A_ AB AB ~ MA * Hence, considering the antecedents as belonging to the triangle OAB, and the consequents to the triangle BAM, we observe that the two sides about the angle A, which is common to both triangles, are proportional ; hence the triangles are similar (373).
EXERCISES. 201 Therefore, ABM is isosceles, since OAB is, and angle BMA = A = OBA, and MB = BA = OM.
This makes 0MB also isosceles, and the angle = OBM. Again, the exterior angle BMA = + OBM = 20; hence, A (which equals BMA) = 20.
What to read after Elementary Geometry Including Plane Solid And Spherical Geometry With Pract?
You can find similar books in the "Read Also" column, or choose other free books by Edward Olney to read onlineMoreLess
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