Free PDF A Treatise on the Line Complex, by C. M. Jessop
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A Treatise on the Line Complex, by C. M. Jessop
Free PDF A Treatise on the Line Complex, by C. M. Jessop
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Originally published in 1903, this book contains a summary of the contemporary research on the theory of line-geometry. Jessop illustrates the text with many diagrams and various examples of how line theory can be applied. This book will be of particular value to anyone with an interest in the history of mathematics.
- Published on: 2015-01-01
- Released on: 2014-12-11
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .87" w x 5.51" l, 1.07 pounds
- Binding: Paperback
- 382 pages
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Most helpful customer reviews
1 of 1 people found the following review helpful.
A waste of time
By Troy learns to design
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.
0 of 1 people found the following review helpful.
prerequisite to understand the Ball's `A treatise on the theory of screws'
By Wangdo Kim
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)
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