## 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 |

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Algebra Applied to Geometry: To Determine the Position of a Point at Rest ... No preview available - 2017 |

Algebra Applied to Geometry: To Determine the Position of A Point at Rest ... X. Y. Z. No preview available - 2009 |

Algebra Applied to Geometry: To Determine the Position of A Point at Rest ... X. Y. Z. No preview available - 2009 |

### Common terms and phrases

abscissa algebraical angular points axis of x centre chord chord is drawn circle radius circle touches circumference co-ordinate axes coincides constant quantity curve cut the axis described touching determine the point direction distance double sign equal equilateral triangle Euclid expression extremity find the area find the equation find the locus geometrical given line Hence isosceles triangle line inclined line is drawn line passing meets the axis middle point moving as follows negative axis negative sign origin parallel particle perpendicular point moves point of contact point of intersection positive axis proposed equation radius vector rectangular axes represent a circle revolves right angle shew side square straight line string substituting t₁ tangent touches the axis touches the positive trace the path transposing Trigonometry values variables vertical diameter x₁ y₁

### 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?