The investigation that Leeuwenhoek recorded in this letter was motivated by another researcher.
Having become acquainted with the various opinions concerning the reproduction of little animals, and more especially with what a certain gentleman has written, who maintains that no living being can originate in a firmly closed bottle, previously filled with meat-juice or meat, I had a mind to make some experiments upon this.
Alle de Brieven / Collected Letters notes that the "certain gentleman" is probably Francesco Redi. His Esperienze intorno alla generazione degli insetti from 1668 had been republished in Amsterdam in 1671 in Latin translation as Experimenta circa generationem insectorum.
After Leeuwenhoek used several glass tubes to carefully control the water, he found many little animals, so small they were barely discernible by his lenses. He could see from the figures in Redi's book that his microscope did not resolve the details that his own did. If the title plate (right) is any indication, Redi used a double-lens microscope that Leeuwenhoek knew would be inferior to his own single-lens magnifiers. He gave Redi the benefit of his doubts.
But I think that when that gentleman speaks of living little animals, he only means worms or maggots, such as we commonly see in rotten meat, and which ordinarily proceed from the eggs of flies and are so large that we have no need of a microscope to discern them.