The theory of epigenesis states that organisms develop from substances present in the egg, which differentiate during embryonic development. This is in conflict with the theory of preformation, which holds that perfect miniature versions of organisms exist in the gametes and grow during development. The idea behind epigenesis can be traced back to Aristotle, who believed that semen was formed from the blood and contained a vital heat which cooked menstrual blood to give rise to offspring. Here, he broke with Hippocrates whose ideas were along the lines of preformation.
Inspired by his experiments on chicken embryos, William Harvey first stated the theory of epigenesis in its modern form in 1651 in his book, Exercitationes de Generatione Animalium (On the Generation of Animals). However, the theory did not easily gain widespread sanction. The Italian physiologist Marcello Malpighi used observational evidence drawn, ironically, from experiments on chicken embryos to back the preformationist view. The fact that it was Malpighi who completed Harvey's theory regarding blood circulation adds further irony to this. Malpighi's assertions were readily accepted by thinkers such as Leibnitz and Malebranche since it conformed to their overall worldviews.
Preformation was finally discredited by the embryologist Casper Wolff in 1759. In his book, Theoria Generationis, he described observations which established that the growth and formation of organs in animals could clearly be observed using microscopes. Specifically, the alimentary canal was absent in early embryos and only appeared in later stages. This settled the debate between proponents of epigenesis and preformation. Once epigenesis gained wide credence, the stage was set for ideas about genetic inheritance and evolution to come to fruition.
Please note that the term 'epigenesis' carries different meanings. Here, it used used in the older sense, as a theory of animal and plant development. In more modern times, it refers to the study of mechanisms by which gene regulation over generations is controlled by elements other than DNA.
King & Cummings. Concepts of Genetics.