Well that's not true. Muslims conquered areas that had collections of Greek and Roman texts. Some of these were translated into Arabic, but translation into Arabic isn't what saved them from being lost. And Muslims were only interested in, or only allowed to be interested in, certain types of Greek and Roman texts.
Most Greek texts that we have today were preserved in the Byzantine Empire, and in other parts of Europe in the Middle Ages. Almost all of the translations we have are direct from the original Greek and Latin, not from Arabic. Some Arabic translations from Greek were used in western Europe in the earlier Middle Ages, but these were replaced with translations direct from Greek when they became available.
I am going to have to agree with Philjames here and defend the tradition of Christendom, both West and East. So upfront, I am going to fully disclose I am a orthodox Catholic in Doctrine (Nicene Creed and Apostles Creed) even though I will mea culpa, mea culpa, mea maxima culpa, say up front have my faults. So my post that follows is through this context and perspective.
I think the Greek texts were all preserved in the Byzantine-Eastern Churches, Modern Eastern Orthodoxy today. Much of the Tradition in the major Eastern Churches in Antioch and Alexandria were part of the Eastern Churches and tradition. The Council of Nicea (Canon 6) gave a primacy to the Churches in Antioch and Alexandria, in their regions, since Rome has always had a primacy. More to the the point, the Church in Alexandria's Liturgy came from Greek Liturgies and has influence of some of the Great Eastern/Greek Doctors (Saint Basil the Great, Saint Gregory of Nazinianus) and also has influence of the Liturgy of Saint Mark the Evangelist. According to Saint Papias, who Saint Irenaeus writing in about 180AD indicates was a pupil and friend of Saint Poycapr, but a hearer of Saint John the Apostle, Saint Mark was in Rome with Saint Peter and his Gospel reflects the preaching of Saint Peter in Rome. The Historian Eusebius notes Mark was the first Bishop of Alexandria. So we have clear Greek texts in Alexandria.
In Antioch, the Greek Liturgy of Saint James is the basis, but there are Syriac (translations) versions of it as well. So much of the Greek texts, both secular and Ecclesial were preserved in Churches under the jurisdiction of Alexandria and Antioch.
When the Muslims conquered former Christian lands in former Eastern Roman empire, they did translate all the Greek texts into Arabic, that is true. As Western Christendom was cut off from the actual Greek texts held in Monastaries, Chruches in the East, Medieval and renaissance Catholics (Western Church) generally only had access to the Arabic translations as they reconquered lands that were invaded by Muslims.
As for the Western Tradition (Latin Text), we have very little extant Ancient Latin writings secular and Catholic that have survived. Rather translations of the extant actual texts. However, I will point out very clearly whether some here like it or not, it was the Church of Rome that preserved all of the Secular and Ecclesial Latin Texts that have come down to us. This occurred partially with the Church of Rome directly but more so with all the Monastic traditions that developed after the Fall of the Western Roman Empire. I will give a shout out to the Benedectines here, even though I am Dominican educated K-8, the Benedictines who were formed in Central Italy about 530 AD, some 50 years after the collapse in Rome, hand copied all the extant Latin Texts that were available to them and passed them down through the centuries.
So I am going to have to respectfully disagree with the narrative that the the Medieval Europeans only rediscovered ancient knowledge because the Arabs preserved it. A few examples we have of preservation of early manuscripts and Christendom to make my point.
The oldest complete Bible we have is the Codex Vaticanus, from mid 4th century and written in Greek. It is at the Vatican. Another ancient Codex, the Codex Alexandrinus, a Greek Bible from 5th century, is the property of the Church of England and British Museum I believe. While there is no original Latin Vulgate of Saint Jerome, the Codex Amiatius has a copy of the Latin Vulgate (oldest we have) that was produced by the Benedictines in England!, how about that, back when you guys were still, oh well, I will be ecumenical here.
, it sometime later was transferred to a Monastery in Florence and is displayed in a museum there, my guess is when King Henry the VIII broke away, lots of the earlier Latin Text were sent back to Rome and the rest of Italy.
The other ancient Codex, the Codex Sinaiticus, another Greek OT and NT, is not in one place, most of it is also in the British Museum. It was probably written in the Levant.
So even with my disclosure up front of my personal religious beliefs, I think the what I wrote does indicate the fact that it was the the Church in both West and East that preserved much of the Latin and Greek texts. Since Greek was the lingua franca in many parts of the Eastern Roman empire and it was the Liturgical language of the Church there, Arabs would have been conversant in Greek and thus able to translate those ancient Greek texts from the primary Eastern Christian Greek sources and bring them with them as they expanded West. That is true. But some of the Monks in the West still spoke some Greek as well so some might have also been translated in the West, Latin obviously and those works were translated by the Church in the West. The Arabs-Muslims did take advantage of the ancient knowledge from the Greeks and Latin text and use it to their advantage, yes.