BO DZING - NORTH WELL


The following is the translation of the ming paragraph headings in North Well 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 twelfth of 18 in the projective geometry series  & was published on January 3, 1956.
This book seems to be about Harmonic & Anharmonic cross ratios used in constructing geometric projections , invariants & the rules thereof. Note: some of the subject links go to the Mathematica website which has some kewl definition of the concepts & terms.
-------------------------------------------------------------------------------------------------------------------
? Link                                   Subject in English
0 Introduction 17th book in the little book series (Ming Dicts + Projective Geo.)
1 Construct Anharmonic divide intersect four arbitrary straight lines
2 Make arbitrary anharmonic divide join four arbitrary points 
3 Affine Solution
4 Cevian construct division
5 Eqality problem - 2 arbitrary parallel lines construct another
6 Duality problem
7 8-point circle example
8 Range multiply rule
9 Involution equality
10 Projectivity problem - find other double point when one is given (redux)
11 Construct projective change equality
12 Example Parabola projectivity
13 Euclidean conjugate example
14 Perspective range projectivity proof
15 Projective straight line make involution 
16 Projective power straight line involution
17 Degenerate power projective condition straight line involution
18 Improper side envelope projection situation
19 Two legs inside circle part finite aribrary division
20 Geometry plane construction project
21 Duality e.g. pencil condition
22 Involution pencil situation
23 Anharmonic conjugate proof of 5-point fixed conic
24 Project straight line with same three principal mean (Brianchonia)
25 Harmonic Regulus duality
26 Cross ratio extends conic pencil
27 One intersetion proof duality
28 Anharmonic conjugate duality example solution
29 Example self duality anharmonic conjugate rule
30 Rule: two projective ranges on different bases are both perspective with the same range on any general line not through their intersection .
31 Polar condition conic example
32 Conic cross ratio condition
33 Construct conic proof 
34 Anharmonic problem
35 First degree example hyperbolic involution
36 Self Involution case (I) 
37 Involution pencil proof maximum rule example
38 4-point change situation (invariants ?)
39 Four part form inside outside degenerate conic situation
40 Porism triangle
41 Ming wen & characters etc. 16th addition to the dictionary
42 Verse from the CHUNG VOO (inmost trust) hexagram in astral script - 13,2

Click here for large picture of the North Well (BO DZING) Cover Design


Tags

  1. north well
  2. projective geometry
  3. bo dzing
  4. ming
  5. cfr

Comments


Mark de LA says
Maybe when we get awe can animate some of the concepts with Cinderella or another tool & provide links to websites that explain the projective geometric concepts to make it easier. On the other hand part of the initiatory virtue of the student exercises is obtained less by memorizing the concepts & more the mathematical thinking . 


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