I. Notes on notation and English terms in 1800s literature (primarily related to series)
The following is from the introductory comments for something involving conditionally convergent series I was working on several years ago.
The logarithm function is often denoted by a lower case L, sometimes italicized (e.g. Catalan's book) and sometimes not italicized (e.g. Laurent's book). Incidentally, this leads to many instances of ln appearing, but these denote the logarithm of $n$ rather than the often now used logarithm function ${\ln}.$ Iterated logarithms were denoted either by consecutive L's or the use of superscripts (e.g. $\ln \ln \ln n$ might be denoted by llln or lll n or ${l^3}n,$ or by similar expressions in which the lower case L is NOT italicized).
$n!$ (factorial) was often denoted by placing $n$ within a "partial box" formed by using only the left and bottom sides of a rectangular box. Anytime you are unsure how factorials are denoted in a book, simply look in places where power series expansions of exponential and trigonometric functions appear. However, most of the time a "factorial notation" was not used, and instead the first few terms (and the general term, if not obvious) were written.
Multiplication was often denoted by a period (easier to typeset than our current centered dot notation), and thus the expression $1.2.3.4$ represents $4! = 24.$
Sometimes an overline bar (called a vinculum) is used instead of parentheses for grouping purposes.
Miscellaneous terms:
vulgar fraction = a quotient of integers written in vertical fraction format
impossible number = non-real complex number
possible number = real number
finite value/quantity = (especially before late 1800s) nonzero value/quantity
absolute term = constant term (e.g. of a polynomial)
numerically greater = absolute value is greater
algebraically greater = greater as signed numbers
contrary signs = opposite signs
vanishing fraction = $0/0$ indeterminate form
integral rational function = polynomial
integral function = power series
development = series expansion
line = curve (e.g. not necessarily a straight line)
right line or straight line = line
curve of $n$ dimensions = curve of algebraic degree $n$
rectilinear asymptote = linear/oblique asymptote
invariable quantity = constant quantity
squared paper = graph paper
the term be wanting = the term is absent
equation is rigorous = exact equality holds
steadily towards = monotonically towards
rigid proof = rigorous proof
- Colloquial journal names:
Annales de Gergonne = Annales de Mathématiques Pures et Appliquées
Crelle's Journal and Borchardt's journal = Journal für die reine und angewandte Mathematik
Darboux's Bulletin = Bulletin des Sciences Mathématiques et Astronomiques [“et Astronomiques” was later dropped]
Grunert's Archiv = Archiv der Mathematik und Physik
Hoffmann's Journal = Zeitschrift fur Mathematischen und Naturwissenschaftlichen Unterricht
Liouville's Journal = Journal de Mathématiques Pures et Appliquées
Terquem's journal = Nouvelles Annales de Mathématiques
II. Glossary of early to mid 20th century terms in some nowhere differentiable continuous functions literature:
The following list is from near the beginning of this mathoverflow answer.
enumerable = countable
unenumerable = uncountable
progressive derivative = right derivative
regressive derivative = left derivative
non-dense = nowhere dense
everywhere dense = dense in the smallest interval containing the set (sometimes “dense”, without being prefaced by “everywhere”, means in context “everywhere dense”)
incrementary ratio = the ordinary difference quotient that a derivative is the limit of
line of invariability (of a function) = an interval on which the function is constant
the set exists = the set is not empty.