An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page xi
If the four points of intersection be all real , all the common chords are real ; if not ,
one pair only is real ON PROJECTIONS . 8 . Definition of Projections 9 .
Projection to infinity 10-12 . Any quadrilateral may be projected , in an infinite
number of ...
If the four points of intersection be all real , all the common chords are real ; if not ,
one pair only is real ON PROJECTIONS . 8 . Definition of Projections 9 .
Projection to infinity 10-12 . Any quadrilateral may be projected , in an infinite
number of ...
Page 57
Prove that the three tangents at their common point meet the sides of the triangle
which intersect their respective conics in three points lying in a straight line ; and
that the other common tangents to each pair of conics intersect the sides of the ...
Prove that the three tangents at their common point meet the sides of the triangle
which intersect their respective conics in three points lying in a straight line ; and
that the other common tangents to each pair of conics intersect the sides of the ...
Page 100
If any two curves be reciprocated , the polar of any point common to both will be a
common tangent to the reciprocal curves , and the pole of any tangent common to
both will be a point of intersection of the reciprocal curves . two curves will ...
If any two curves be reciprocated , the polar of any point common to both will be a
common tangent to the reciprocal curves , and the pole of any tangent common to
both will be a point of intersection of the reciprocal curves . two curves will ...
Page 105
Hence the first thing to be proved is , “ That the three straight lines joining the
points of contact of the common tangent with the angular points of the triangle not
lying on the respective conics all pass through a point . ” Again , “ the other ...
Hence the first thing to be proved is , “ That the three straight lines joining the
points of contact of the common tangent with the angular points of the triangle not
lying on the respective conics all pass through a point . ” Again , “ the other ...
Page 106
Hence the latter part of the theorem will run : “ And that the same three straight
lines respectively join the other point of intersection of each pair of conics with the
angular point of the triangle common to each pair . ” 11. After a little practice , the
...
Hence the latter part of the theorem will run : “ And that the same three straight
lines respectively join the other point of intersection of each pair of conics with the
angular point of the triangle common to each pair . ” 11. After a little practice , the
...
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Common terms and phrases
angle angular points appears Author become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coefficients coincide College common condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine distance draw drawn eliminating equal equation Examples expressed find the equation fixed point focus follows given point given straight line gives harmonic Hence imaginary line at infinity locus meet observed obtained opposite sides pair parabola parallel passing pencil perpendicular point of intersection points of contact polar pole positive produced projection prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree sides similar Similarly student taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written
Bibliographic information
| Title | An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
| Author | Norman Macleod Ferrers |
| Edition | 4 |
| Publisher | Macmillan and Company, 1861 |
| Original from | Sapienza University of Rome (Biblioteca di Matematica G. Castelnuovo) |
| Digitized | 2 May 2013 |
| Length | 184 pages |
| Export Citation | BiBTeX EndNote RefMan |