What is the Book of Nature?
The Book of Nature is a concept that comes from the ancient Greek philosophers and early Christian theologians. It is the idea that nature contains a revelation for the existence of God just as the Bible does. The ancient Greek culture influenced our modern western world more than any other classical civilization. Their culture gave us democracy, math, science, philosophy, architecture, art, literature, and most importantly Christianity. Greece was one of the first Christian nations of the Roman empire, which spread both Greek culture and the Christian religion to a large part of the ancient world. Just before the arrival of the Christian apostles, the Greeks were hard at work rediscovering the natural world around them through science and philosophy, no doubt by divine providence,
The Greek philosophers began reconstructing a model of the natural world in which all references to mythological origins had been removed. By abandoning ties to immoral, petty, and conspiring gods of nature, Greek philosophers accidentally left the upper world vacant. The new ideas and philosophy of nature made the mythological forces of Zeus and the old gods irrelevant. While some philosophers began embracing atheism, others began investigating the new concept of a single divine being, also known as monotheism. How exactly they came to this happen only a few hundred years before the arrival of Christianity cannot be a coincidence.
Xenophanes (born in 470 BC) was one of the first philosophers to claim there were not many gods but one supreme God. He was a harsh critic of those who held polytheistic gods to be truly divine, arguing that only the One could be truly divine. 
"God is one, supreme among gods and men, and not like mortals in body or in mind."
- Xenophanes 
How he came to this conclusion is somewhat obscure, however it may have been an idea that was circulating in philosophical circles before he wrote about his belief. However this belief, which does not appear to have come from the ancient Jewish people, who were the only worshippers of the one true God at this time. This ancient philosopher's statement does seem to give credence to the Apostle Paul's teaching in the Book of Romans, that God is evident to all people even if they have never heard of him.
The wrath of God is being revealed from heaven against all the godlessness and wickedness of people, who suppress the truth by their wickedness, since what may be known about God is plain to them, because God has made it plain to them. For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse. For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. Although they claimed to be wise, they became fools and exchanged the glory of the immortal God for images made to look like a mortal human being and birds and animals and reptiles.
Xenophanes was certainly not the only monotheist among the Greek philosophers. Socrates came later (born in 469 BC) and openly spoke about a single God of unknown identity, that may have been the Christian God.  Socrates was very outspoken about the gods of the ancient Greeks being immoral beings, just as Xenophanes and others before him. He claimed that God must be the greatest good in every conceivable way, including morally. Because of this, he said people should stop listening to the poets (ancient pagan preachers such as Homer). However unlike the other philosophers who became monotheists he may have been too outspoken about his beliefs. He was tried and executed for impiety towards the traditional gods of the ancient Greeks. In one of Plato's greatest works, The Republic, he quotes Socrates' line of thinking on becoming a monotheist.
"Neither, if we mean our future guardians to regard the habit of quarrelling among themselves as of all things the basest, should any word be said to them of the wars in heaven, and of the plots and fightings of the gods against one another, for they are not true... Then God, if he be good, is not the author of all things, as the many assert, but he is the cause of a few things only, and not of most things that occur to men. For few are the goods of human life, and many are the evils, and the good is to be attributed to God alone; of the evils the causes are to be sought elsewhere, and not in him... Then we must not listen to Homer or to any other poet who is guilty of the folly of saying that two casks lie at the threshold of Zeus, full of lots, one of good, the other of evil lots... Shall I ask you whether God is a magician, and of a nature to appear insidiously now in one shape, and now in another --sometimes himself changing and passing into many forms, sometimes deceiving us with the semblance of such transformations; or is he one and the same immutably fixed in his own proper image?... Then it is impossible that God should ever be willing to change; being, as is supposed, the fairest and best that is conceivable, every god remains absolutely and for ever in his own form." - Socrates, quoted by Plato, The Republic, Book II
Several ideas in this passage spoken by Socrates agree with the Christian scriptures, including the idea that God is the source of goodness, that bad things happen to humanity because of their own evil deeds, that the gods of the ancient Greeks are not true gods, and that God cannot change.  Interestingly Socrates also referenced the 'image of God' which is a name for Jesus Christ, who would not be born for another 400 years.  The Bible describes "spiritual warfare" between angels and demons in various places, it may be that Socrates and other philosophers were being influenced by the spiritual realm.
Aristotle came later (born in 384 BC) and advanced one of the most influential logical arguments for God until William Paley wrote the watch maker analogy in 1802 AD, over two thousand years later. Aristotle theorized that everything in the universe has a cause, and those causes must have had a cause, and so on. He believed that this chain of causes could not go back infinitely, but there must have been an original cause to the universe. He called this first cause the Prime Mover in his book Metaphysics.
"The first principle and primary reality is immovable, both essentially and accidentally, but it excites the primary form of motion, which is one and eternal. Now since that which is moved must be moved by something, and the Prime Mover must be essentially immovable, and eternal motion must be excited by something eternal... but the primary essence has no matter, because it is complete reality. Therefore the Prime Mover, which is immovable, is one both in formula and in number; and therefore so also is that which is eternally and continuously in motion." - Aristotle, Book 12 Metaphysics
Many ancient Greek philosophers seems to agree with the Apostle Paul, that God is evident through his creation. It seems that on several occasions, at least in recorded history, human beings were able to logically deduce his existence. It would follow that perhaps many more times this happened and it was not recorded in the history books. The Book of Hebrews in the Bible records Abraham leaving the pagan nation he was born into and seeking to the find which city-state had the true God.  Obviously this got God's attention, perhaps because the entire world was pagan when Abraham was born. Because of this, God revealed himself to Abraham and made him a prophet and the father of the entire Jewish people. Perhaps Abraham came to a similar logical and philosophical conclusion as Xenophanes, Socrates, and Aristotle.
It has long been speculated by Christian theologians, beginning with Thomas Aquinas, that God has given two types of revelation to mankind. One type is known as special revelation, which is any revelation from a supernatural event which includes prophesy, scripture and the Bible, and any miracles. The other type of revelation is general revelation, which is available to all of mankind, and is what the Apostle Paul references in Romans 1:18-23. It is the idea that the grandeur of the creation suggests that only a super intelligent mind could be responsible for the universe, and therefore all of mankind is guilty if they do not seek out and worship the true God. This has also been called by theologians the Book of Nature, as though nature itself spoke of the creator like a book of the Bible.
It seems that the monotheistic philosophers of ancient Greece were evidence that the Apostle Paul and Christian theologians are correct in their assertions of the existence of general revelation or the Book of Nature. The first documented use of the term was from Galileo , and then was later used by theologians such as Augustine and Conrad of Megenberg. Since the Middle Ages, the Book of Nature has been referenced metaphorically by philosophers, theologians, and scholars of all walks of life. In the centuries that followed many works referenced the Book of Nature as a new authority concerning the divine, including The Assayer by Galileo, The Mathematical Principles of Natural Philosophy by Isaac Newton, Harmonies of the World by the astronomer Johannes Kepler, The Excellency of Theology, Compared with Natural Philosophy by Robert Boyle, and Novum Organum by Sir Francis Bacon.
The heavens declare the glory of God;
the skies proclaim the work of his hands.
Day after day they pour forth speech;
night after night they display knowledge.
There is no speech or language
where their voice is not heard.
Their voice goes out into all the earth,
their words to the ends of the world.
1. McKirahan, Richard D. "Xenophanes of Colophon. Philosophy Before Socrates. Indianapolis: Hackett Publishing Company, 1994. 61. Print.
2. Laërtius, Diogenes (1925). "Others: Xenophanes" . Lives of the Eminent Philosophers. Vol. 2:9. Translated by Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.
3. Cantrell, Michael A. (2014) "Was Socrates a Christian Before Christ? Kierkegaard and the Problem of Christian Uniqueness," Faith and Philosophy: Journal of the Society of Christian Philosophers: Vol. 31 : Iss. 2 , Article 1. DOI: 10.5840/faithphil20146210 Available at: https://place.asburyseminary.edu/faithandphilosophy/vol31/iss2/1
4. God is the source of goodness - Mark 10:18
We suffer because of sin - John 5:14
Pagan gods are not true gods - Jeremiah 16:20
God does not change - Malachi 3:6
5. Colossians 1:15-17
6. Hebrews 11:10
7. Evernden (1992), p. 52