SAH KUK - MILLET VALLEY


The following is the translation of the ming paragraph headings in Millet Valley which represents a table of contents of the book by CFR. You can click on the numbers which will take you to the Ming Translator if you don't like my interpretation. Note in the book itself there are references to the Tai Shu which is a privately published set of documents where the material was originally developed & published to a limited circle of friends.
This book is the 13th of 18 in the projective geometry series  & was published on February 14, 1956.
This book seems to cover a lot of collineation, projectivity hyperbolic & elliptic, perspective involutions & is the substance of what I imagine geometricians would cream their jeans for! Some of the tools so far are used all together.
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? Link                          Subject in English
0 Introduction & decode of the name of this book SAH KUK (Millet Valley)
1 Porism (Proposition) : Triangle Self Duality
2 Outside inside polygon form
3 4 points & lines situation
4 Involution situation
5 Conic inside triangle - side with same 3 points 
6 Way to make equal angle
7 Design similar triangle inside a circle
8 Make Collineation projection - elation & homology 
9 General homology construct hyperbolic projectivity  etc. Euclidean 
10 Elliptic projectivity example
11 collineation corresponding Hyperbolic projectivity conic
12 Another example conparing anharmonic conjugates
13 Involution example extends hyperbolic
14 Same degree duality
15 Coordinates collineation duality
16 Coordinates collineation duality begin proper conic
17 Harmonic collineation self uses proper conic
18 Same degree improper conic involution axis 
19 Self coordinates collineation construct elliptical projectivity using proper conic involution axis
20 Perspective collineation functional correspondence 
21 Harmonic perspective collineation 
22 Another Harmonic design example with arbitrary finite perspective center
23 Projective collineation functional correspondences 
24 Collineation example
25 Collineation with fixed conic
26 Maximum degree curve situation make conic (Pascalia and Gergonne)
27 Third degree curve rule
28 Use conic intersection to make tangent rule (some cf Hessian #s)
29 Parametric collineation            (+ new ming wen)
30 Curvature collineation
31 Conic focus directrix collineation 
32 Effective involution
33 Cyclic Collineation
34 Harmonic mates conic example (some cf Pascalia)
35 Stretch example
36 Projective involution compare to classic design
37 Proper conic - make double point coprojective involution condition straight line
38 Imaginary double point
39 Another drawing
40 Make tangent using transormational equation

Click here for large picture of SAH KUK (Millet Valley) cover design


Tags

  1. millet valley
  2. sah kuk
  3. projective geometry
  4. ming
  5. cfr

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