An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... Theorem EXAMPLES 280 68 70 CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the Point in which a Straight Line , drawn in a given direction through a given Point of the Conic , meets the ...
... Theorem EXAMPLES 280 68 70 CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the Point in which a Straight Line , drawn in a given direction through a given Point of the Conic , meets the ...
Page x
... Theorem 103 тоб 13 . · 15-17 . Reciprocation with respect to a Circle The anharmonic ratio of the Pencil , formed by ... Theorems by Reciprocation with respect to a circle ib . 21 . Corresponding Points and Lines . The angle between the ...
... Theorem 103 тоб 13 . · 15-17 . Reciprocation with respect to a Circle The anharmonic ratio of the Pencil , formed by ... Theorems by Reciprocation with respect to a circle ib . 21 . Corresponding Points and Lines . The angle between the ...
Page 58
... 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 59
... theorem will be proved to be true for all deter- minants . 4. Next , suppose we have the three equations + = b ̧ï ̧ + b ̧ï ̧ + b ̧ï ̧ = 0 , С1X2 + С ̧X2 + ¤â¤ ̧ = 0 . Multiply these equations in order by the arbitrary multi- pliers ...
... theorem will be proved to be true for all deter- minants . 4. Next , suppose we have the three equations + = b ̧ï ̧ + b ̧ï ̧ + b ̧ï ̧ = 0 , С1X2 + С ̧X2 + ¤â¤ ̧ = 0 . Multiply these equations in order by the arbitrary multi- pliers ...
Page 64
... theorem is true for a determinant of n rows , if it be true for one of n - 1 . But it is true for three rows , therefore it is uni- versally true . 7. The horizontal rows of a determinant are commonly spoken of as " lines , " the ...
... theorem is true for a determinant of n rows , if it be true for one of n - 1 . But it is true for three rows , therefore it is uni- versally true . 7. The horizontal rows of a determinant are commonly spoken of as " lines , " the ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα