The author of the book you are quoting was a Big Time Liberal, who was trying to show in his book how Anti-Science Christianity was and how necessary it was to push it out of universities.
The book that's being cited in your post (I wonder if you aren't just copying and pasting this from a website) "A History of the Warfare of Science with Theology in Christendom," is commonly said to be poorly supported. So, it/whatever source you have, may not be as credible a source as you think for assessing the actual positions of EVERY SINGLE CHURCH FATHER (THERE ARE LOTS). Most people claim that many Church Fathers never spoke on the topic.
However, when it comes to Science contradicting The Scripture, we have a duty to defend Scripture, if we can. Otherwise, we have a duty to submit, which implies that we have a duty to The Truth. So, it matters if The Earth is Flat or a Globe and Moving or Stationary, particularly since Scripture implies a Flat and Stationary Earth, which everyone knows, it's just that some people want to say it is figurative, which of course the language doesn't seem figurative and the actual science seems to point towards a flat and stationary Earth. And we have centuries of known conspiracy against The Faith.
So, we have a crime that needs to be set right and the authority to do it, regardless of what Church Fathers thought about it, before 749 A.D. It is encouraging though, that some actually preached on it and were Flat Earthers.
The author of the book I quoted is a Protestant. However, his quotes are accurate when quoting the Fathers on their teachings. Dickenson White is long recognized for having "proven" the Church wrong about flat earth, and for making Her look stupid for doing it. His attempt to prove how wrong the Church was, actually provides many sources for Church teachings on the subject. White's sources are, as far as I've checked, totally accurate when quoting Catholics on the subject of flat earth. Remember, he's trying to make them look bad, quoting them directly, as though popular science he espouses trumps what the Church has always taught. What White winds up doing is showing from his sources, that even from the Protestant historical perspective, the Catholic Church has always promoted the geocentric flat earth, because he draws from Catholic teachings and saints in order to provide the "damning" material.
Beyond White's book, I also quoted from a book on Catholic homilies.