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

BY

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

REGIUS PROFESSOR OF DIVINITY IN THE UNIVERSITY OF DUBLIN.

SIXTH EDITION.

London:

LONGMANS, GREEN, AND CO.

1879.

CAMBRIDGE:

PRINTED BY W. METCALFE AND SON, TRINITY STREET AND ROSE CRESCENT.

esipi-
mis 9.0 Read
12 14-1931

CONTENTS.

[Junior readers will find all essential parts of the theory of Analytical Geometry included

in Chapters I., II., V., VI., X., XI., XII., omitting the articles marked with asterisks.]

Coordinates of Point cutting that Distance in a given Ratio .

Transformation of Coordinates

does not change Degree of an Equation

Polar Coordinates

Two Equations represent Points

A single Equation represents a Locus

Geometric representation of Equations

Equation of a Right Line parallel to an Axis

through the Origin

in any Position

Meaning of the Constants in Equation of a Right Line

Equation of a Right Line in terms of its Intercepts on the Axes

CHAPTER II.

THE RIGHT LINE,

11

12

13

14

15

16

17

18

in terms of the Perpendicular on it from Origin, and the Angles it makes

Expression for the Angles a Line makes with Axes

Equation of Line joining two given Points

Condition that three Points shall be on one Right Line

Coordinates of Intersection of two Right Lines

Middle Points of Diagonals of a Quadrilateral are in a Right Line (see also p. 62) 26

Equation of Perpendicular on a given Line

of Perpendiculars of Triangle

of Perpendiculars at Middle Points of Sides

of Line making a given Angle with a given Line