Linear Polars of the K Hedron in N Space

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. . , ^).
Any line through the point of intersection of p{ and qi is given by the equation 7 ^^^+aiai, x = o, ii= I, 2j • • • aj /£/ where a, - are arbitrary constants.
These equations are all identical for ai= so that all the points 'Cf. Cayley, "Sur quelques th6oremes de la geometric de position, " Collected Works, I, 360.
lO LINEAR POLARS OF THE ^-HEDRON IN W-SPACE {pi qi), (i=i, 2, . . . . , k) are collinear on the line 1 = 1 which is the equation of the polar line of P as to the ^-line \pi
...\.
§ 9. The linear polar point of a point as to a linear point ^-ad. Given point P : (x'l, x'z, o) and points Pi : a, fa;=o, (j=i, 2, . . . . , li) on line p : 0:3 = 0.
Pass the lines pi : 0^5^ = through the points Pi. The polar line of P as to the ^-line {pi\ is the Hne « = i and q intersects p in the point •^ "■!. A;' t = i which is the equation of the polar point of P as to the ^-ad \Pi\. § 10. The MacLaurin generalized definition of harmonic mean.
Let OQ=y = — represent the distance from some fixed point taken as origin on a given line to any point Q of the line af^ For the point Pi : af^x=o y= — ^ .


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