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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? 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.

MAR SIANG - HORSEBACK

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