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A TREATISE

ON

CONIC SECTIONS:

31

CONTAINING

AN ACCOUNT OF SOME OF THE MOST IMPORTANT MODERN
ALGEBRAIC AND GEOMETRIC METHODS.

BY

GEORGE SALMON, D.D., D.C.L., F.R.S.,

REGIUS PROFESSOR OF DIVINITY IN THE UNIVERSITY OF DUBLIN,

Fifth Edition.

LONDON:

LONGMANS, GREEN, READER, AND DYER.

1239

1869.

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Length of Perpendicular from a Point on a Line

Equations of Bisectors of Angles between two given Right Lines
Area of Triangle in terms of Co-ordinates of its Vertices

Area of any Polygon

Condition that three Lines may meet in a Point (see also p. 34)
Area of Triangle formed by three given Lines

·

Equation of Line through the Intersection of two given Lines

CHAPTER III.

EXAMPLES ON THE RIGHT LINE.

Investigation of rectilinear Loci .

of Loci leading to Equations of Higher Degree

Problems where it is proved that a Moveable Line always passes through a

Fixed point

Centre of Mean Position of a series of Points

Right Line passes through a Fixed Point if Constants in its Equation be
connected by a Linear Relation

Loci solved by Polar Co-ordinates

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Trilinear Co-ordinates

Trilinear Equation of Parallel to a given Line

of Line joining two Points

Proof that middle Points of Diagonals of Quadrilateral lie in a Right Line

Intersections of Perpendiculars, of Bisectors of Sides, and of Perpendiculars at
middle points of Sides, lie in a Right Line (see also pp. 60, 127)

Equation of Line at infinity

Cartesian Equations a case of Trilinear

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66

Angle between two Lines given by a single Equation

Equation of Bisectors of Angles between these Lines

Condition that Equation of second Degree should represent Right Lines (see also

pp. 144, 148, 150, 255)

Number of conditions that higher Equations may represent Right Lines
Number of terms in Equation of nth Degree

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