Solutions of the Examples in a "sequel to Elementary Geometry"
Solutions of the Examples in a "sequel to Elementary Geometry"
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In our eReader you can find the full English version of the book. Read Solutions of the Examples in a "sequel to Elementary 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 Solutions of the Examples in a "sequel to Elementary Geometry"
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Invert w. r. to 0. Then inverts into the pt r at infinity on P'^. Hence (/'iT, P'Q') is h« .'. Bf bisects the common tangent P^Q^. Hence B^ lies on the r. a.
Hence the locus of B is the O through 0, coaxal with the given O".
Ex. 17. Invert w. r. to any pt. on the JL O, r. Then r becomes the common diameter of a\ h\ c\ Obviously the O coaxal with a% V through P' touches Hence the G coaxal with a, h through P touches c Ex. 18. Invert w. r. to A. Then the given O^ &, c invert into the || |" V, d, ...outside which A lies ; the variable O x becomes a^, a O touching V^ d ; the inverse of il w. r. to re becomes the centre of of. Now the locus of the centre of of i&9k\d' half-way between V and c^ Hence the locus of the inverse of J. is a O e2 touching h, c at A. Let the ± from A to b\ c\ dl cut them at ^, G\ iX. Then 2/cJ = 1/6 + 1/c if 2 Aiy = ABf + 4C' (by p. 110) ; and this is true.
Ex. 19. Invert w. r. to an int^ of the given O* a, 6. Then the variable O" a?, y become O^ of, yf touching the j* a', V in the same angle.
What to read after Solutions of the Examples in a "sequel to Elementary Geometry"?
You can find similar books in the "Read Also" column, or choose other free books by Russell, John Wellesley, 1851- to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Invert w. r. to 0. Then inverts into the pt r at infinity on P'^. Hence (/'iT, P'Q') is h« .'. Bf bisects the common tangent P^Q^. Hence B^ lies on the r. a.
Hence the locus of B is the O through 0, coaxal with the given O".
Ex. 17. Invert w. r. to any pt. on the JL O, r. Then r becomes the common diameter of a\ h\ c\ Obviously the O coaxal with a% V through P' touches Hence the G coaxal with a, h through P touches c Ex. 18. Invert w. r. to A. Then the given O^ &, c invert into the || |" V, d, ...outside which A lies ; the variable O x becomes a^, a O touching V^ d ; the inverse of il w. r. to re becomes the centre of of. Now the locus of the centre of of i&9k\d' half-way between V and c^ Hence the locus of the inverse of J. is a O e2 touching h, c at A. Let the ± from A to b\ c\ dl cut them at ^, G\ iX. Then 2/cJ = 1/6 + 1/c if 2 Aiy = ABf + 4C' (by p. 110) ; and this is true.
Ex. 19. Invert w. r. to an int^ of the given O* a, 6. Then the variable O" a?, y become O^ of, yf touching the j* a', V in the same angle.
What to read after Solutions of the Examples in a "sequel to Elementary Geometry"?
You can find similar books in the "Read Also" column, or choose other free books by Russell, John Wellesley, 1851- to read onlineMoreLess
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