An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
From inside the book
Page 1
We shall usually denote the angular points of the triangle of reference by the
letters A , B , C , the lengths of the sides respectively opposite to them by a , b , c ,
and the distances of any point from BC , .CA , AB respectively by the letters a , b ,
y .
We shall usually denote the angular points of the triangle of reference by the
letters A , B , C , the lengths of the sides respectively opposite to them by a , b , c ,
and the distances of any point from BC , .CA , AB respectively by the letters a , b ,
y .
Page 7
It hence may be proved that the three straight lines , drawn through the angular
points of a triangle to bisect the opposite sides , intersect in a point . For these
straight lines will be represented by the equations or b = oy , cy = an , αα = bß ,
and ...
It hence may be proved that the three straight lines , drawn through the angular
points of a triangle to bisect the opposite sides , intersect in a point . For these
straight lines will be represented by the equations or b = oy , cy = an , αα = bß ,
and ...
Page 8
To find the equation of the straight line drawn through one of the angular points of
the triangle of reference , perpendicular to the opposite side . sar Making a
construction similar to that in the last proposition , it will be seen that we have
here an ...
To find the equation of the straight line drawn through one of the angular points of
the triangle of reference , perpendicular to the opposite side . sar Making a
construction similar to that in the last proposition , it will be seen that we have
here an ...
Page 9
It will however be observed , that if Q and B lie on the same side of AC , Q and C
will lie on opposite sides of AB , and vice versa . Hence , if QK = B , QL = -9 . siWe
have therefore gle wn B + y = 0 as the equation of the line AQ , which externally ...
It will however be observed , that if Q and B lie on the same side of AC , Q and C
will lie on opposite sides of AB , and vice versa . Hence , if QK = B , QL = -9 . siWe
have therefore gle wn B + y = 0 as the equation of the line AQ , which externally ...
Page 30
... respectively intersect the sides opposite to them , lie in the same straight line ;
and that the points in which the external bisector of any one angle and the
internal bisectors of the other two angles , intersect the sides respectively
opposite to ...
... respectively intersect the sides opposite to them , lie in the same straight line ;
and that the points in which the external bisector of any one angle and the
internal bisectors of the other two angles , intersect the sides respectively
opposite to ...
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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 |