# Algebra Applied to Geometry: To Determine the Position of a Point at Rest, the Locus of a Moving Point, the Equation to the Straight Line, and the Equation to the Circle

E. Johnson, 1843 - Equations - 96 pages

### Popular passages

Page 92 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Page vii - IF any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 90 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the...
Page vii - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 88 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Page 79 - If a straight line touch a circle, the straight line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle.
Page vii - In a circle the angle at the centre is double the angle at the circumference, standing upon the same arch ; BDC = 2 B AC.
Page 22 - ... the locus of the points which are at the same distance from a fixed point, or of a point which moves so as to be always at the same distance from a fixed point, is a circle ; conversely a circle is the locus of the points at the same distance from a fixed point, or of a point moving so as to be always at the same distance from a fixed point ; and so, in general, a curve of any given kind is the locus of the points which satisfy, or of a point moving so as always to satisfy, a given condition.
Page 89 - The straight line drawn from the centre to the middle point of a chord is perpendicular to the chord.
Page 68 - ... is the locus of a point moving in a plane at a constant finite distance from a fixed point in that plane, and its equation is я?