# 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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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

- spring palace
- projective geometry
- ming
- jun koong
- cfr

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