About 2,230 results
|Translated into many languages, this book was in continuous use as the standard university-level text for a quarter-century, until it was revised and enlarged by the author in 1952.|
|Florentin Smarandache University of New Mexico, Gallup, NM D1111, USA |
Abstract In this article we prove the theorems of the orthopole and we obtain,
through duality, its dual, and then some interesting specific examples of the dual
of the ...
|(i) To begin, let's investigate what happens to the orthopole when the line m is |
moved parallel to itself. Let P\ be the orthopole of m\ relative to AABC (Figure 162
; any two of the defining perpendiculars LX, MY , and NZ suffice to determine an ...
|If q = b \b'c'.b'c', r = c\b'c'.b'c', then [q Wb' . r ifc'ar\ is the orthopole of the line ab'c' |
for a' be. Since [qra] = o, we have an equation similar to (8) : [a Wa' . q |*V . . a Wb'
. r \b'c' ..qWb'.r U'a'] = o. But [q▒b'c'] = [bWc'l thence [a \c'a' .q \b'c'] is the ...
|The common point of (JJ, 7g)-orthoprojective lines discussed in the Lemma we |
will call the projective orthopole. Let a conic section containing the points Ii, 1%
be given. The above determined transformations & and dp'1 map the conic on the
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