Does 'develop' in "In Chapter 2 we develop essential aspects of elliptic curve cryptography." strike you as not the right word? [closed]

The quote in question comes from the Introduction, page 12, to this book:

In our quest for comprehensiveness, we have chosen to present all the basic elements of cryptography needed to understand the complexities of Monero, and their mathematical antecedents. In Chapter 2 we develop essential aspects of elliptic curve cryptography.

I have found that develop can mean to discover, find out; to uncover. Is it the intended meaning? If so are there any other resources that would corroborate such meaning of develop? I cannot help thinking about rewriting this sentence with another word, such as cover or discover, like so:

In our quest for comprehensiveness, we have chosen to present all the basic elements of cryptography needed to understand the complexities of Monero, and their mathematical antecedents. In Chapter 2 we cover essential aspects of elliptic curve cryptography.

Solution 1:

One common enough use of this verb in scientific literature is the following, where mostly "explanation" is concerned, the addition of ideas is not a constructive addition but an addition of known facts that haven't yet been mentioned.

(OALD) idea/story/musical theme ​[transitive] develop something to add further explanation or details to an idea, story or musical theme
SYNONYM elaborate
♦ She develops the theme more fully in her later books.
♦ The piano then takes up the melody and develops it.
♦ He began to develop these ideas in a series of paintings.

In your sentence this is not exactly the meaning that is intended; it is not either the following, plain meaning.

(OALD) ​ [intransitive, transitive] to gradually grow or become bigger, more advanced, stronger, etc.; to make something do this

The exact meaning is not found in this dictionary, but it appears in the SOED (Shorter Oxford English Dictionary)

(SOED) develop 2 Uncover, reveal (something immaterial or (obsolete) material); make known, bring to light; discover; detect, find out. Now US. [since] mid 18th century

Since this book seems to be issued from American authors, the "Now US" label, which means "only used in the US nowadays", makes it the most likely meaning (essentially, "reveal", "make known", "bring to light").

This is a definition very similar to the one found in the Merriam Webster dictionary, which is an American dictionary, but that you do not find either in OALD, Collins, or lexico which are British dictionaries.

a: to set forth or make clear by degrees or in detail : EXPOUND develop a thesis

This is so a fortiori because "aspect" in the case of a scientific phenomenon is not an appearance that could be more or less changeable but a fixed feature that one is not likely to change unless the theory is reckoned with as lacking in some respect.

It is true that the connotations of the plain meaning are not so pleasant but it is also true that the shift from this plain meaning to the relevant one is an accomplished thing. If one finds those connotations too spurious one can use the prepositional verb "to cover", or the more literary and imaged "discover".

Solution 2:

Have a look at this definition:

4a: to cause to evolve or unfold gradually : to lead or conduct (something) through a succession of states or changes each of which is preparatory for the next

/developed his argument

From here

Unlike cover, which is straight forward and just means include, talk about, develop carries the idea of gradually building up from the fundamentals and taking the reader through the process of discovering or working it out.