From French logistique, from Ancient Greek λογιστικός (logistikós, “practiced in arithmetic; rational”), from λογίζομαι (logízomai, “I reason, I calculate”), from λόγος (lógos, “reason, computation”), whence English logos, logic, logarithm, etc.; modern mathematical use influenced by related logarithmic. Sense of “logistic function” by Pierre François Verhulst (1845) in French, then borrowed into English. Verhulst does not explain his choice of naming, but he contrasts it with the logarithmic curve (also from λόγος (lógos)), and it is presumably by analogy with arithmetic and geometric (other divisions of mathematics), as his discussion of arithmetic growth and geometric growth precede his discussion of logistic growth. The term logistic and logistical also found occasional mathematical use in English prior to 1800, from the same Greek origin.
If we compare the calculus of a triangle, by the logistic logarithms …1730 July, J. P. Biester, “Decreasing Logarithms”, in The Present State of the Republick of Letters, volume 6, page 103:
From French logistique, from Ancient Greek λογιστικός (logistikós, “practiced in arithmetic; rational”), from λογίζομαι (logízomai, “I reason, I calculate”), from λόγος (lógos, “reason, computation”), whence English logos, logic, logarithm, etc.; modern mathematical use influenced by related logarithmic. Sense of “logistic function” by Pierre François Verhulst (1845) in French, then borrowed into English. Verhulst does not explain his choice of naming, but he contrasts it with the logarithmic curve (also from λόγος (lógos)), and it is presumably by analogy with arithmetic and geometric (other divisions of mathematics), as his discussion of arithmetic growth and geometric growth precede his discussion of logistic growth. The term logistic and logistical also found occasional mathematical use in English prior to 1800, from the same Greek origin.
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Mathematics, Sciences A logistic function or graph of a logistic curve.