NavList:

I think that we are talking about a subject that we can call navigational mathematics. It had conventions that navigators understood. An example is the tillde ~. It appears from time to time in navigational textbooks. I can sort of guess what it means but have never seen a satisfactory explanation. It is complicated by sometimes having a + or - symbol above it. It was used by Cloudy Weather Johnson in a 1906 edition of his famous book.

I believe that by the 1920s the writers of navigational books understood negative numbers. In 1920 Blackburne  talks about adding + and - symbols to numbers and then says "take the elgebraic sum". Or if you read the derivation of the haversine formulas from the cos formula it seems obvious that the writer understands algebra. Sometime between about 1850 and 1900 there must have been a change from text formulas to algebraic formulas. The former are dfficult for modern eyes to undersand. I do not have sufficiant books of ths period to decide when/how the change ocurred.

David C