Why is logistic equation called

• Why is logistic equation called “logistic”?
  https://math.stackexchange.com/questions/357918/why-is-logistic-equation-called-logistic

The fact that the name was "given by Verhulst" does not explain why it was given. Usually people pick names for a reason, but maybe Verhulst was an exception. Ok, I looked at the French wikipedia, which states "Le nom de courbe logistique leur a été donné par Verhulst sans que l'on sache exactement pourquoi." - "The name "logistic curve" was given to it by Verhulst, but no one knows exactly why". The reference rasch.org gives the following commentary:

"Verhulst writes "We will give the name logistic [logistique] to the curve" (1845 p.8). Though he does not explain this choice, there is a connection with the logarithmic basis of the function. Logarithm was coined by John Napier (1550-1617) from Greek logos (ratio, proportion, reckoning) and arithmos (number). Logistic comes from the Greek logistikos (computational). In the 1700's, logarithmic and logistic were synonymous. Since computation is needed to predict the supplies an army requires, logistics has come to be also used for the movement and supply of troops. So it appears the other meaning of "logistics" comes from the same logic as Verhulst terminology, but is independent (?). Verhulst paper is accessible; the definition is on page 8 (page 21 in the volume), and the picture is after the article (page 54 in the volume). "

• What does the name “Logistic Regression” mean?# What does the name “Logistic Regression” mean?

As it has been already pointed out, ''logistic'' comes from logistic curve/function/distribution (which is underlying logistic regression). So the question is: where is logistic coming in their names?
The reference to Verhulst (i.e. Wikipedia's statement) seems a bit false. While it is clearly true that it is most widely attributed to Verhulst, the first actual use seems to come from Edward Wright. See Thompson: On Growth and Form (1945), page 145. (Found via the well-known Earliest Known Uses of Some of the Words of Mathematics page.)

Thompson hints that Verhulst used it in connection with its S-shape, but gives no clue about Wright.

However, given that one of the most important parts of Wright's work was pertaining to logarithms, it seems logical that he used it as a reference to logarithm. Indeed (and more precisely), the 1911 edition of Encyclopaedia Britannica refers to the old mathematical term logistic number:

The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign.

Also note that logarithm itself comes from proportion (logos) + number (arithmos); originally coined by John Napier.

So, I believe, this is the most likely explanation: ''logistic'' is used in Wright's time in connection with what we now call ''logarithm'', which was used by Wright when he constructed that curve.