Elements of Quaternions |
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Page xv
... chords , drawn from the given point p Pages . 554-559 * In this Article , or Series , 397 , and indeed also in 396 and 398 , several re- ferences are given to a very interesting Memoir by M. de Saint - Venant , " Sur les lignes courbes ...
... chords , drawn from the given point p Pages . 554-559 * In this Article , or Series , 397 , and indeed also in 396 and 398 , several re- ferences are given to a very interesting Memoir by M. de Saint - Venant , " Sur les lignes courbes ...
Page xviii
... chords ( 397 ) from that point ; equation ( p . 590 ) of a cylinder of the second order , which has an arbitrary line PE from P as one side , and has contact of the fourth order ( or five - point contact ) with the curve at P ; the ...
... chords ( 397 ) from that point ; equation ( p . 590 ) of a cylinder of the second order , which has an arbitrary line PE from P as one side , and has contact of the fourth order ( or five - point contact ) with the curve at P ; the ...
Page xix
... chords from P ; the cone thus found may be called the Osculating Oblique Cone ( comp . 397 ) , of the second order , to that cone of chords ; and the coefficients of its equation in- volve only r , r , r ' , r ' , r " , r " , but not r ...
... chords from P ; the cone thus found may be called the Osculating Oblique Cone ( comp . 397 ) , of the second order , to that cone of chords ; and the coefficients of its equation in- volve only r , r , r ' , r ' , r " , r " , but not r ...
Page xxiii
... chords ( 397 ) from P ; while the other tangent plane to the cubic cone ( C3 ) crosses that first plane ( P ) , or the quadric cone ( C2 ) , at an angle of which the trigonometric cotan- * Compare the first Note to p . 609 of these ...
... chords ( 397 ) from P ; while the other tangent plane to the cubic cone ( C3 ) crosses that first plane ( P ) , or the quadric cone ( C2 ) , at an angle of which the trigonometric cotan- * Compare the first Note to p . 609 of these ...
Page xxxii
... chord PP ' is per- pendicular to its own polar . ( b ) . Under the same conditions , if the point P be given , the locus of the chord PP ' is usually ( p . 676 ) a quadric cone , say ( C ) ; and there- fore the locus of the point r ' is ...
... chord PP ' is per- pendicular to its own polar . ( b ) . Under the same conditions , if the point P be given , the locus of the chord PP ' is usually ( p . 676 ) a quadric cone , say ( C ) ; and there- fore the locus of the point r ' is ...
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Common terms and phrases
ABCD algebra angle anharmonic arbitrary axis centre chord coefficients collinear comp Compare the Note complanar cone conic conjugate considered constant construction cubic cubic equation cyclic cylinder deduced denote derived differential diplanar direction ellipsoid equal expression formula function geometrical given curve given point harmonic conjugate imaginary intersection length line OA linear lines of curvature locus multiplication normal notation osculating circle osculating plane P₁ perpendicular positive quadric quinary quotient radius reciprocal rectangular represented respect right line right quaternions right quotient rotation round satisfied scalar second order SECTION sides sphere spherical sub-articles supposed surface symbol tangent plane tensor ternions theorem tion transformation twisted cubic vector versor vertex VIII whence whereof write