Researchers on Curves of the Second Order by George Whitehead Hearn - PDF

Book Contents :-
1.1 Problem proposed by Cramer to Castillon 1.2 Tangencies of Apollonius 1.3 Curious property respecting the directions of hyperbolæ; which are the loci of centres of circles touching each pair of three circles 2.1 Locus of centres of all conic sections through same four points 2.2 Locus of centres of all conic sections through two given points, and touching a given line in a given point 2.3 Locus of centres of all conic sections passing through three given points, and touching a given straight line 2.4 Equation to a conic section touching three given straight lines 2.5 Equation to a conic section touching four given straight lines 2.6 Locus of centres of all conic sections touching four given straight lines 2.7 Locus of centres of all conic sections touching three given straight lines, and passing through a given point, and very curious property deduced as a corollary 2.8 Equation to a conic section touching two given straight lines, and passing through two given points and locus of centres 2.9 Another mode of investigating preceding 2.10 Investigation of a particular case of conic sections passing through three given points, and touching a given straight line; locus of centres a curve of third order, the hyperbolic cissoid 2.11 Genesis and tracing of the hyperbolic cissoid 2.12 Equation to a conic section touching three given straight lines, and also the conic section passing through the mutual intersections of the straight lines and locus of centres 2.13 Equation to a conic section passing through the mutual intersections of three tangents to another conic section, and also touching the latter and locus of centres 2.14 Solution to a problem in Mr. Coombe’s Smith’s prize paper for 1846. 3.1 Equation to a surface of second order, touching three planes in points situated in a fourth plane 3.2 Theorems deduced from the above 3.3 Equation to a surface of second order expressed by means of the equations to the cyclic and metacyclic planes 3.4 General theorems of surfaces of second order in which one of M. Chasles’ conical theorems is included 3.5 Determination of constants 3.6 Curve of intersection of two concentric surfaces having same cyclic planes 3.7 In an hyperboloid of one sheet the product of the lines of the angles made by either generatrix with the cyclic planes proved to be constant, and its amount assigned in known quantities 3.8 Generation of cones of the second degree, and their supplementary cones 3.9 Analytical proofs of some of M. Chasles’ theorems 3.10 Mode of extending plane problems to conical problems 3.11 Enunciation of conical problems corresponding to many of the plane problems in Chap. II 3.12 Sphero-conical problems

About this book :-
This is a classic mathematical work that provides a rigorous study of "conic sections and second-order curves". The book examines ellipses, parabolas, hyperbolas, and related curves, offering both theoretical insights and practical methods for analysis. It is an essential resource for students, educators, and researchers seeking a deeper understanding of "analytic geometry" and its applications. Hearn systematically explores the classification and properties of second-order curves, including tangencies, intersections, and special geometric cases. His approach combines clear explanations, historical context, and numerous examples to make complex concepts accessible. Detailed proofs and propositions illustrate fundamental principles, making the text valuable for anyone interested in the foundations of geometry and the mathematical techniques of the 19th century. Its structured presentation, rigorous analysis, and emphasis on clarity make it a timeless reference in the study of conic sections and analytic methods. Hearn’s work continues to influence mathematics education and research, bridging classical geometry with modern analytical approaches while remaining relevant for learning, teaching, and exploration of geometric theory.

Book Detail :-
Title: Researchers on Curves of the Second Order by George Whitehead Hearn - PDF
Publisher: Macmillan & Co.
Year: 1846
Pages: 64
Type: PDF
Language: English
ISBN-10 #: 1293004545
ISBN-13 #: 978-1293004548
License: Public Domain Work
Amazon: Amazon

About Author :-
The author George Whitehead Hearn was a 19th-century mathematician and educator specializing in "analytic geometry". He focused on the study of "conic sections and second-order curves", providing detailed proofs and analytical methods that became foundational in the field. Hearn’s work combined mathematical rigor with clear exposition, making complex geometric concepts accessible to students and scholars alike. He is best known for his 1846 publication, "Researches on Curves of the Second Order", which systematically explores ellipses, parabolas, hyperbolas, and other second-order curves. Hearn’s contributions remain a valuable reference for "geometry, analytic methods, and mathematics education", bridging classical and modern approaches.

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