Chapters on the Modern Geometry of the Point, Line, and Circle, Vol. 1 (Classic Reprint): Being the Substance of Lectures Delivered in the University ... of the First Year in Arts (Classic Reprint) - Softcover

Inhaltsangabe

This book explores the modern geometry of points, lines, and circles, providing a solid foundation for understanding the fundamentals of this branch of mathematics. The author presents a systematic approach, assuming readers have basic knowledge of Euclidean geometry. The book covers various concepts, including the concept of double acceptance of geometrical terms, allowing magnitudes to be represented by numbers or letters, and the simultaneous determination of linear reciprocals. It also addresses the peculiarities of evanescent and infinite values of magnitudes. The author discusses the theory of maxima and minima, introducing the notions of extreme maximum and minimum values, the concept of positive and negative in geometry, and the use of the biliteral notation to indicate direction as well as magnitude. They explore the theory of the mean center of any system of points for any system of multiples, focusing on its importance in mechanics and highlighting instances where the mean center is indeterminate. Finally, the book examines topics such as complete and incomplete figures of points and lines, collinear and concurrent systems of points and lines, the theory of inverse points with respect to a circle, and the theory of poles and polars with respect to a circle, offering a comprehensive treatment of the subject.

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