JUN KOONG - SPRING PALACE

The following is the translation of the ming paragraph headings in Spring Palace 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 sixth of 18 in the projective geometry series  & was published on May 14, 1955.
Note the term Pascalia (CFR uses this term for Pascal Lines designs ) has a nice link at Wolfram - the purveyor of Mathmatica. They also have decent definitions of some of the other projective geometry & mathmatical terms . This book covers topics like projectivity, involution, secants, harmonic ratio, conjugates, duality, perspective, & vectors.

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Paragraph Link                  Subject in English
0 Introduction & derivation of book name - exponents ?
1 Double contact point conic family with same involution axis
2 Construct tangent use conic pencil
3 Two united secants cross contact point - divide harmonic separate family conic
4 Double contact point family tangent harmonic method
5 Secant mean hyperbola asymptote equality
6 Three double contact point conic
7 Divide harmonic secant rule 
8 Self conjugate triangle resolve circle tangent with same conic center rule
9 Compare proper-improper double contact point angle pencil tangent rule
10 Contact point problem (tangent duality)
11 Conjugate example solve tangent problem with same arithmetic design affine p9
12 Conic with same three points
13 Invert point make angle unit circle join diameter limit  the bisect angle
14 Design of corresponding double contact point conic path (pg 12)
15 Corresponding circle path
16 Unit circle rectangular resolves harmonic condition
17 Another harmonic example
18 Another double contact point example 
19 Circle secant perspective center ?. Self duality harmonic rule
20 Harmonic mates point unit conic join construct mates straight line
21 Arithmetic design inverts rule
22 Invert Angle
23 Circle 4-point invert condition
24 Another invert rule (& on next page harmonic path)
25 Harmonic envelope
26 Conic Directrix 
27 Proper harmonic path self conjugate triangle
28 Degenerate harmonic envelope extends two affine circle
29 Apollonius Hyperbola reaches point
30 Parabola Rule
31 Two perspective triangle
32 Construct double contact point envelope
33 Ellipse , Hyperbola case 3D correspendences 
34 Two project 4 points 
35 Projective Example
36 Perspective Example 
37 Coefficient divide
38 Vector exact crossing rule
39 Resolve circle 9 point circle extends the exact crossing family
40 Unity
41 Join equal walk parabola involution axis case
42 Conic self-conjugate triangle 4-point case

Click here to see large version of book cover


Tags

  1. spring palace
  2. projective geometry
  3. ming
  4. jun koong
  5. cfr

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