An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page ix
... Theorem EXAMPLES 287 ib . 69 71 CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND DEGREE . 2 . 3 . To find the point in which a straight line , drawn in a given direction through a given point of the conic ...
... Theorem EXAMPLES 287 ib . 69 71 CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND DEGREE . 2 . 3 . To find the point in which a straight line , drawn in a given direction through a given point of the conic ...
Page x
... Theorem 112 13 . The anharmonic ratio of the Pencil , formed by four intersect- ing straight lines , is the same as that of the range formed by their poles 113 15 . Any straight line drawn through a given point A is divided harmonically ...
... Theorem 112 13 . The anharmonic ratio of the Pencil , formed by four intersect- ing straight lines , is the same as that of the range formed by their poles 113 15 . Any straight line drawn through a given point A is divided harmonically ...
Page xi
... Theorems by Reciprocation with respect to a point ib . 123 31 . 33 . Corresponding Points and Lines . The angle between the radius vector and tangent in any curve is equal to the cor- responding angle in the Reciprocal Curve Co ...
... Theorems by Reciprocation with respect to a point ib . 123 31 . 33 . Corresponding Points and Lines . The angle between the radius vector and tangent in any curve is equal to the cor- responding angle in the Reciprocal Curve Co ...
Page 59
... theorems as will be necessary in our future investigations ; referring the reader who may be desirous of fuller informa- tion to Salmon's Lessons on the Higher Algebra ; Spottis- woode , On Determinants ( the second edition of which ...
... theorems as will be necessary in our future investigations ; referring the reader who may be desirous of fuller informa- tion to Salmon's Lessons on the Higher Algebra ; Spottis- woode , On Determinants ( the second edition of which ...
Page 60
... theorem will be proved to be true for all deter- minants . 4. Next , suppose we have the three equations + = b1x1 + b2x2 + bâxq = 0 , 2 C11 + С2x2 + С3x3 = 0 . Multiply these equations in order by the arbitrary multi- pliers 60 ...
... theorem will be proved to be true for all deter- minants . 4. Next , suppose we have the three equations + = b1x1 + b2x2 + bâxq = 0 , 2 C11 + С2x2 + С3x3 = 0 . Multiply these equations in order by the arbitrary multi- pliers 60 ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²