# MAR SIANG - HORSEBACK

The following is the translation of the ming paragraph headings in Horseback 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 tenth of 18 in the projective geometry series & was published on October 11, 1955.

This book is heavy on the calculation conics & the corresponding algebra & drawings on the Affine & Euclidean planes. This is the beginning of integrating many tools & concepts into one drawing.

Some of it is a mix of English & Ming with the first few paragraphs provided in both to help the student translate the mathematical & geometric metaphors (contexts) from Ming to English.

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This book is the tenth of 18 in the projective geometry series & was published on October 11, 1955.

This book is heavy on the calculation conics & the corresponding algebra & drawings on the Affine & Euclidean planes. This is the beginning of integrating many tools & concepts into one drawing.

Some of it is a mix of English & Ming with the first few paragraphs provided in both to help the student translate the mathematical & geometric metaphors (contexts) from Ming to English.

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? Link | Subject in English |

0 | Introduction & decode of book name MAR SIANG |

1 | Exact circle harmonic rule |

1' | Orthogonal circles harmonic rules (in English) |

1.1 | Conversely let two lambda & chi circles be orthogonal ?. |

1.1' | " in English |

1.2 | ** |

1.2' | Any number of points on circle called "concyclic" ?.. |

1.3 | Solving an equation |

1.4 | Further Rule |

1.5 | Poles and polars |

2.0 | Begin draw Euclidean parabola ?..elliptic involution |

2.1 | Orthogonal circles harmonic rules (in English) |

2.2 | Lines through elliptic involution (TTP) meet at right angles |

2.3 | Orthocyclic, Concyclic and involution conditions |

3.0 | Orthogonal circles algebraic calculation |

3.1 | General equation of any circle |

3.2 | Formula for cosine of an angle of circular intersection in terms of constants ? |

4.0 | Three orthogonal circles, common diameter end polar rule |

4.1 | Equation solved with determinants & polar form coordinates |

5.0 | Self conjugate triangle rules |

5.1 | Algebraic proof |

5.2 | Conjugate points situation |

5.3 | Two #s on radical axis, conjugate on one circle of coaxality are conjugate ? |

5.4 | Proof |

6.0 | Examples of angle functions (trigonometry?) |

7.0 | Calculating conic as an equilateral hyperbola on affine plane |

8.0 | Inequalities & inequation |

9.0 | Number Principles |

10.0 | Multiplication involution |

11.0 | General properties of numbers demonstrated on calculating design |

12.0 | Square roots (+/-) & inequalities |

13.0 | More inequalities & square roots |

14.0 | Table of useful formulae for use with calculations |

15.0 | Right angle triangle equation solution |

16.0 | Proof Ptolemy rule with same calculating design |

17.0 | New secant solves equation |

18.0 | Harmonic rule example - affine working with several rules on same drawing |

19.0 | Four tangent circle rule |

20.0 | Ellipse intersetion question |

21.0 | Area of triangle = product of 3 sides divided by 2x circumdiameter ? |

22.0 | Euler Rule |

23.0 | Harmonic tangent rule |

24.0 | Circle & rectangular hyperbola construction problem |

25.0 | Anharmonic divide & cross ratios |

26.0 | Anharmonic change rule |

27.0 | Divide distance rule |

28.0 | Unified harmonic calculations |

29.0 | The drawing |

30.0 | Harmonic cross ratio make tangent |

31.0 | Anharmonic Example & the tropermic algorithm + extensions |

32.0 | Caution unity of heaven & earth in the divine name is goal (i.e. Great Work!) |

Click here for large picture of Horseback (MAR SIANG) cover design | |

** | It looks like Horseback begins a different numbering system with inter paragraph translation into English at this point . There is a primed number for the English which I will use instead of the ming translator at this point. Also CFR seems to have left out topic headers for some of the paragraphs. |

### Tags

- horseback
- projective geometry
- ming
- mar siang

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