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Analytical Conics (Dover Books on Mathematics)

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undefinedThis concise text introduces students to analytical geometry, covering basic ideas and methods. Readily intelligible to any student with a sound mathematical background, it is designed both for undergraduates and for math majors. It will prove particularly valuable in preparing readers for more advanced s. The text begins with an overview of the analytical geometry of the straight line, circle, and the conics in their standard forms. It proceeds to discussions of translations and rotations of axes, and of the general equation of the second degree. The concept of the line at infinity is introduced, and the main properties of conics and pencils of conics are derived from the general equation. The fundamentals of cross-ratio, graphic correspondence, and line-coordinates are explored, including applications of the latter to focal properties. The final chapter provides a compact account of generalized geneous coordinates, and a helpful appendix presents solutions to many of the examples.

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