An Elementary Treatise On Determinants, With Their Application to Simultaneous Linear Equations And Algebraical Geometry

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III. Prop, III.
.'. the 3 Lines do not intersect in one Point, but there are 2 of them which intersect in one Point, and in one only.
(Pnop. IIL (1) (2) If -B = ; and if there be, among the Equations to the 3 Lines, 2 which have their F-Block not evanescent ; then the Equations are consistent, and there is only one set of values for the Variables ; (Ch. III. Prop. VIIL the 3 Lines intersect in one Point, and in one only""'.
(3) If B = ; and if every 2 of the Equations to the 3 Lines have their
...F-Block evanescent ; and if there be among them 2 which have their 5- Block not evanescent ; then 2 of the Lines are parallel ; (Prop. III. (2) and the 3 have the same direction. (Prop. III. (4) (4) If every 2 of the Equations to the 3 Lines have their ^-Block evanescent ; (.whence also ^ = 0) ; then the 3 Lines coincide. (Prop. III. (3) From (2), (3), and (4) may be deduced (5) lf^ = 0; then the 3 Lmes intersect in one Point at a finite or infinite distance.
From (2) and (4) may be deduced * Prop.


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