A sequel to the first six books of the Elements of Euclid containing an easy introduction to modern geometry, with numerous examples. (Part I) / by John Casey.

Format:

Book

Author/Creator:

Casey, John.

Series:

Dublin University Press series.

Nineteenth Century Collections Online: Science, Technology, and Medicine, Part I.

Dublin University Press series

Nineteenth Century Collections Online: Science, Technology, and Medicine, Part I

Language:

English

Subjects (All):

Geometry.

Physical Description:

1 online resource ([xv], 166 p.) : ill.

Other Title:

Sequel to the first six books of the Elements of Euclid

Place of Publication:

Dublin : Hodges, Figgis & Co. ; London : Longmans, Green & Co., 1910 (Ponsonby and Gibbs)

Contents:

bk. I. section I. Bisecting points of sides of triangles and quadrilaterals

Middle point of diagonals of quadrilaterals

Loci of vertices of triangles

given bases and sum of areas

Concurrence of perpendiculars of triangles

Perpendiculars from extremities of base on bisector of vertical angle of a triangle

Perpendiculars at middle points of sides of a triangle

Inscribed and escribed squares to a triangle

Centre of mean position

Maxima and minima

Deducibles from Euclid, fig., Prop. XLVII

section II. Exercises

bk. II. section I. Rectangle contained by segments of base of an isosceles triangle

Sums of squares of sides of triangles and quadrilaterals

Rectangle contained by sum and difference of two sides of a triangle

Euler's theorem with respect to four collinear points

Perpendiculars let fall from angular points of a square on a line

Theorem on the squares of sides of a triangle whose base is divided in a given ratio

Properties of sum of multiples of squares of lines drawn to a variable point from any number of given points

bk. III. section I. Properties of two circles touching each other

Common tangent to two circles

Rectangles of non-corresponding sides of two equiangular triangles

Properties of perpendiculars from any point of a circle on two tangents and chord of contact

Properties of perpendiculars form any point of a circle on sides of an inscribed quadrilateral

Feet of perpendiculars on sides of a triangle from any point in circumscribed circle are collinear

Intercepts of perpendiculars of a triangle between point of concurrence and circumscribed circle are bisected by the sides of the triangle

Property of line joining any point in circumference of a circle to the intersection of perpendiculars of an inscribed triangle

Problems on maxima and minima

Philo's line

Centre of instantaneous rotation

Inversions and orthogonal circles defined

Easy propositions on coaxal circles

Easy propositions on poles and polars

Problems on construction of triangles

bk. IV. section I. Intercepts between angular points of a triangle and points of contact of inscribed and escribed circles in terms of sides

Area of triangle in terms of sides

Sum of perpendiculars from any point on the sides of a regular polygon

Sum of perpendiculars on any line from angular points of a regular polygon

Sum of squares of distances from any point to angular points of a regular polygon

"Nine-points circle" of a triangle

Propositions relating to circumscribed circle to a triangle

Special multiples for mean centres of angular points of a triangle

bk. VI. section I. Properties of segments of sides of a triangle made by concurrent lines

Properties of segments of sides of a triangle made by collinear points

Rectangle of two sides of a triangle

Property of perpendiculars on sides and diagonals of inscribed polygon

Locus of vertex of a triangle when base and ratio of sides are given

Property of a parallel to one of the sides of a quadrilateral through intersection of diagonals

Property of distances of vertices of a triangle from centres of inscribed and escribed circles

Relation between radii of inscribed and circumscribed circles of a triangle

Properties of centres and axes of perspective of two triangles

Solutions of geometrical problems

section II. Centres of similitude

section III. Theory of harmonic section

section IV. Theory of inversion

Extension of Ptolemy's theorem

section V. Coaxal circles

section VI. Theory of anharmonic section

section VII. Theory of poles and polars, and reciprocation

section VIII. Miscellaneous exercises.

Notes:

Includes index.

Reproduction of the original from the Huntington Library.

Includes bibliographical references.

OCLC:

866987247