Index of the Propositions Used in Book 7 of Pappus' Collection
Ken SAITO

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Symbols for Propositions in Part 1

5. Index: Part 1

Symbols for propositions in Part 1

Each proposition begins with one of the following symbols that indicate:

1 to 13	volume number of the Euclidean Elements.
44 to 321	paragraph number in Pappus Book 7.
Con	Apollonius' Conics
Data	Euclid's Data
DetSection	Apollonius' deteminate section
Menelaus	the so-called Menelaus' theorem
Pappus	other volumes of Pappus's Collection
Sect.Spatii	Apollonius' Cutting off of an area

Hence, for example,

2-5	Elements, volume 2, prop. 5.
Con-1-11	Conics, volume 1, prop. 11.

• Dir and Conv (conv)
• Proposition 6-16 consists of an enunciation (6-16-Dir) and its converse (6-16-Conv). The converse of 3-35, which is not stated in the Elements but is used by Pappus, is referred to as 3-35-conv (note the difference of Conv and conv).
• A, B.
• Proposition 5-7 consists of two enunciations which are not converses reciprocally. They are referred to as 5-7-A, 5-7-B
• Cor
• Corollaries are indicated by Cor.
• x, x2, lem, cor, ..., x-conv,
• For extensions of a proposition, x, x2, ... are used. If the extension is concerned with inequality while the proposition itself deals with equality, "ineq" is used insted of "x". Some other extentions are classified as lemma (lem) and corollary (cor). Therefore, 3-35-x, 5-17-ineq, 6-23-lem, etc.
• Data
• Data-27 means Data proposition 27, of course. Some results of the type "if X is given, then Y is given" are used though not stated in the Data. In this case, the proposition that would justify this result is mentioned with the word "Data" added after, e.g., 5-12-Data.

• 2-A, 2-B, 5-B, 5-P, 5-Q.