Algebraical Geometry

Excerpts

• Algebraical Geometry

  If two straight lines be drawn at right angles to each other, dividing the whole of their plane into four parts, one lying in each right angle, the situation of any point is determined when we know, (1) in which angle it lies, and (2) its perpendicular distances from the two right lines.

• Algebraical Geometry

  for, though there is an infinite number of points whose distance from $OA$ only is the same as that of $P$, and an infinite number of others, whose distance from $OB$ is the same as that of $P$, there is no other point whose distances from both lines are the same as those of $P$.

• Algebraical Geometry

  The line $OA$ is called the axis of $x$, because it is usual to denote any variable distance measured on or parallel to $OA$ by the letter $x$.

• Algebraical Geometry

  It is moreover usual to call the co-ordinate $OM$, the *abscissa*, and $MP$, the *ordinate*, of the point $P$.

• Algebraical Geometry

  As $O$ moves towards $A$, the point $P$ will, by its motion on $MP$, compounded with the motion of the line $MP$ itself, describe a curve $OP$, in which $PM$ is less than, equal to, or greater than, $OM$, according as $OM$ is less than, equal to, or greater than the linear unit.

Equations

• Algebraical Geometry

  y = x^{2}

  The ordinate y of a moving point P is always equal to the square of its abscissa x, so P traces a parabola (the book's example of a curve given by a function).

Problems

No exercises in this chapter.