The following is the translation of the ming paragraph headings in Dragon Pearls 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 first in the projective geometry series of 18 & was published on January 17, 1955.
The subject of this book is all about the geometry of tangents . The other subjects covered in the process are: inversion, polar coordinates, Affine & Euclidean drawings, centroids, & vectors.
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0	Introduction - Condensed rules to make tangents
1	Circle Construct
2	Polar Involution make tangent
3	Five angle rule is rudicible Pascalia way to make tangent
4	Triangle construct
5	Conjugate point way
6	Working Design
7	Tangent from outside point to a conic
8	Fluxion - Differential coefficient = tangent
9	Inverted affine Hjelmslev example
10	Ellipse curvature circle
11	Three degree rule
12	Arithmetic design (may be a key to CFR's calculating circle invention)
13	3D unity formula
14	Regulus rule
15	Two 4-point fixed point opposite geometric plane project
16	Complete 3D five point geometric surface secant rule
17	Polar condition conic
18	Centroids
19	Harmonic Centroid forumula
20	Reducible hyperbola vector condition
21	Euclidean Affine circle tangent
22	Euclidean & Affine circle root tangent straight line rule
23	Finite Circles cross
24	Function corresponding 5-star rule - divine equal parts
25	Euclidean/Affine ellipse by Circle Focus condition
26	Make polar case conic reach two perspective triangle
27	Two imaginary fixed elliptic involution double point intersection
28	Gage rule conic
29	Small inversion path to join two points
30	Affine rectangular (..way) to make new conic element bring self duality
31	Within triangle conic mates with circle focus (circle inscribed in a triangle)
32	Center perspective rule
33	Five point projection to make conic
34	Wind 3D kite tower pagoda way to construct vector