Thomas Robert Malthus is a 18th century demographer and economist that is famous for the study of population growth, especially for the support of laws that would limit the growth of (poor) population. The basis of his reasoning is summarized by Wikipedia:
The main point of his essay was that population multiplies geometrically and food arithmetically, therefore whenever the food supply increases, population will rapidly grow to eliminate the abundance.
On which basis are these two claims in bold funded?
The fact that a population grows geometrically (in other words, exponentially) in a situation of abundance of resources is now classic and known as the exponential growth or natural growth. This Wikipedia page claims that the model was in fact introduced by Malthus himself.
Why did Malthus consider that resources grow arithmetically?
Actually, the same Wikipedia page quotes Malthus (emphasis added):
"Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. ... The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds."
The text does not mention arithmetic but bounded resources. It is more in line with a logistic model with a constant carry capacity, or seasonal variations.
Did Malthus really consider resources growing arithmetically, or is it a later misattribution?