The phrase "popularly supposed" can be replaced with a variety of synonyms. Some options include "widely believed," "commonly thought," "generally accepted," "popularly assumed," and "frequently purported." These phrases all convey the idea that there is a prevailing belief or idea about a certain subject, without necessarily implying that it is true or accurate. Other possible synonyms might include "generally understood," "conventionally held," or "traditionally believed." These variations in phrasing can help a writer avoid repetition and add nuance to their language, while still conveying the same basic meaning.