A sequel to the first six books of the Elements of Euclid
Subtitle: containing an easy introduction to modern geometry, with numerous examples. (Part I)
By: by John Casey
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
Publisher: Hodges, Figgis & Co.; Longmans, Green & Co.
Published: 1910
Place of publication: Dublin; London
Language: eng
Format: [electronic resource] :
Number of pages: 166
Subjects: Geometry
Other titles: Sequel to Euclid
Notes: Includes index.

Reproduction of the original from the Huntington Library.

Includes bibliographical references.
Table of contents: title: bk. I. section I. Bisecting points of sides of triangles and quadrilaterals; title: Middle point of diagonals of quadrilaterals; title: Loci of vertices of triangles; title: given bases and sum of areas; title: Concurrence of perpendiculars of triangles; title: Perpendiculars from extremities of base on bisector of vertical angle of a triangle; title: Perpendiculars at middle points of sides of a triangle; title: Inscribed and escribed squares to a triangle; title: Centre of mean position; title: Maxima and minima; title: Deducibles from Euclid, fig., Prop. XLVII; title: section II. Exercises; title: bk. II. section I. Rectangle contained by segments of base of an isosceles triangle; title: Sums of squares of sides of triangles and quadrilaterals; title: Rectangle contained by sum and difference of two sides of a triangle; title: Euler's theorem with respect to four collinear points; title: Perpendiculars let fall from angular points of a square on a line; title: Theorem on the squares of sides of a triangle whose base is divided in a given ratio; title: Properties of sum of multiples of squares of lines drawn to a variable point from any number of given points; title: section II. Exercises; title: bk. III. section I. Properties of two circles touching each other; title: Common tangent to two circles; title: Rectangles of non-corresponding sides of two equiangular triangles; title: Properties of perpendiculars from any point of a circle on two tangents and chord of contact; title: Properties of perpendiculars form any point of a circle on sides of an inscribed quadrilateral; title: Feet of perpendiculars on sides of a triangle from any point in circumscribed circle are collinear; title: Intercepts of perpendiculars of a triangle between point of concurrence and circumscribed circle are bisected by the sides of the triangle; title: Property of line joining any point in circumference of a circle to the intersection of perpendiculars of an inscribed triangle; title: Problems on maxima and minima; title: Philo's line; title: Centre of instantaneous rotation; title: Inversions and orthogonal circles defined; title: Easy propositions on coaxal circles; title: Easy propositions on poles and polars; title: Problems on construction of triangles; title: section II. Exercises; title: bk. IV. section I. Intercepts between angular points of a triangle and points of contact of inscribed and escribed circles in terms of sides; title: Area of triangle in terms of sides; title: Sum of perpendiculars from any point on the sides of a regular polygon; title: Sum of perpendiculars on any line from angular points of a regular polygon; title: Sum of squares of distances from any point to angular points of a regular polygon; title: "Nine-points circle" of a triangle; title: Propositions relating to circumscribed circle to a triangle; title: Special multiples for mean centres of angular points of a triangle; title: section II. Exercises; title: bk. VI. section I. Properties of segments of sides of a triangle made by concurrent lines; title: Properties of segments of sides of a triangle made by collinear points; title: Rectangle of two sides of a triangle; title: Property of perpendiculars on sides and diagonals of inscribed polygon; title: Locus of vertex of a triangle when base and ratio of sides are given; title: Property of a parallel to one of the sides of a quadrilateral through intersection of diagonals; title: Property of distances of vertices of a triangle from centres of inscribed and escribed circles; title: Relation between radii of inscribed and circumscribed circles of a triangle; title: Properties of centres and axes of perspective of two triangles; title: Solutions of geometrical problems; title: section II. Centres of similitude; title: section III. Theory of harmonic section; title: section IV. Theory of inversion; title: Extension of Ptolemy's theorem; title: section V. Coaxal circles; title: section VI. Theory of anharmonic section; title: section VII. Theory of poles and polars, and reciprocation; title: section VIII. Miscellaneous exercises.