A Treatise on the Line Complex Classic Reprint C M Jessop 9781440047909 Books
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CHAPTER 1. SYSTBIS OF COORDIXATBS. 1. Ix the analyticn.1 treatment by Des Cartos of the Geometry of Spa.ce, the point is the ~plce-clcment; the researches of PODcclct and other geometers, and in pnrticular the Priociplc of Duality, ICld llaturally to the plane' as a space-clemellt; finally to PlUcker- 1S du(; the conception of a geometry in which t.hc line serve~ as the clement of space. Just as the point ~l-lld phtne arc defineu by coordinates and the in"cstigation of loci of points and envelopes of plalles is conducted by Igebl'r.ical lllethod~ ill the older gcometry, so in that with which this work is cOlleerned, line-coordinates are employed. a.nd loci of lines nrc by their means discussed. The object of the present treatise is then, mainly, the illvestigation of the propeltics of the assemblage of lines which satisfy olle Or more given conditions, i.e. of lines whose coordinates satisfy olle 01' more equatiolJs of given form. If only one condition is
Table of Contents
ART; II, III; i,', ~; ,i-x; xi-xiv; XY, xyi; xvii; 2-9; 10-1J; 14; 15-1G; 17; 18; 19-21; 22; 23; 24; ~2i-27; 28; 20; CONTEN'l'S,; INTRODUCTION,; Double ratio; Cnl'I'CSI'OldellCe of poillts on the samc li1lf~; Im'olntion; COn'csponciences 011 difrCruut lin~; Collillc,tion; Involutions OJ! D curve; (2, 2) C01TC8}londcnce~; CHAPTER 1; SY~TE~lS OF COORDlKATE~,; Definition of complex and congruence; Systcms of COOrdillllte;; Pencil, sheaf
A Treatise on the Line Complex Classic Reprint C M Jessop 9781440047909 Books
I don't think the style of the book will suit modern readers, especially when there is few to none figures in the book, which is probably due to the difficulty of drawing them without the help of modern computers. Besides, it is my understanding that many cumbersome classical analytic geometry can be elegantly reduced to linear algebra of matrices. A very successful example is Pottmann's Computational Line Geometry.People who come to this book are probably readers of Ball's A Treatise on the Theory of Screws. In this case, I feel responsible to say that there is nothing more that be can extracted beyond the level of K.H. Hunt's Kinematic Geometry of Mechanisms. Going through tons of linear/quadratic equations simply will do no good, and may even destroy one's mathematical sharpness. This is no healthy mathematics, just a waste of your time. People who recommended this are the publishers of the book.
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A Treatise on the Line Complex Classic Reprint C M Jessop 9781440047909 Books Reviews
Reading C. M. Jessop's `A treatise of the Line Complex' is prerequisite to understand the Ball's `A treatise on the theory of screws'. It is somewhat coincident because each book was published in 1903 and 1900 respectively.
Jessop adopted Klein coordinates as the analytical method of treatment. He thought that the success of Plücker researches was limited by the unsuitable (Cartesian) analysis he employed.
The subject owes its origin to Plücker, the author of the book, the New Geometries des Raumes, Plücker introduces the conception of a complex of lines, i.e., the Infinites in three dimensions of lines which satisfy one given condition. His work contains most of the chief properties of such complexes
Jessop illustrated the simplest form of the complex as screw motion
a12(xy'-yx')+a34(z-z')=0
If in this equation z and z' be increased by any quantity h the equation is not altered, i.e., a complex lime may be translated in any way parallel to the axis without ceasing to belong the complex also, xy'-yx' is unaltered by a rotation of the line about the axis, hence if all the lines of a complex are subjected to a screw motion about the axis, the complex itself is not unaltered.
Also a pitch is defined as -a23/a12=r tan (theta)
Above all, This book states the utmost important concept which may have huge potential on Joint Biomechanics. "Involution"
On any line common to two linear complexes a(1,1) correspondence of points is determined by the planes through the line,viz. by taking the poles of each plane for the two complexes. If a certain condition, connecting the constants of the equations of the two complexes, is satisfied,these pairs of points form an involution.
I don't think the style of the book will suit modern readers, especially when there is few to none figures in the book, which is probably due to the difficulty of drawing them without the help of modern computers. Besides, it is my understanding that many cumbersome classical analytic geometry can be elegantly reduced to linear algebra of matrices. A very successful example is Pottmann's Computational Line Geometry.
People who come to this book are probably readers of Ball's A Treatise on the Theory of Screws. In this case, I feel responsible to say that there is nothing more that be can extracted beyond the level of K.H. Hunt's Kinematic Geometry of Mechanisms. Going through tons of linear/quadratic equations simply will do no good, and may even destroy one's mathematical sharpness. This is no healthy mathematics, just a waste of your time. People who recommended this are the publishers of the book.
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