Generally, I hate to quote scripture. Most Buddhist sutras are very old, from a time when many were illiterate. There is a form to these sutras that is designed, as an aid to memorization, to insure that the main points are transmitted properly. They have a beginning that often identifies the speaker, the place/time, and the audience. The speaker(s) in most cases are representative of positions and are not necessarily the words spoken by the real historical figure named. For instance, Ananda was one of the Buddha's closest and most loving disciples, so he is identified as the speaker in some sutras written long after his death. Was Ananda the actual speaker, or is he just a convenient mouthpiece for a doctrinal point of later Buddhist theologians? Most folks have no idea who these various personalities are, and one hesitates interpolating a long explanation of who and what these folks represent to Buddhist scholars. These old forms are very repetitive. The same phrase is used over and over again at the beginning or end of each refrain. Sometimes the same formulistic expression will have minor variations, each of which is intended to explicate some small element of the primary theme of the sutra. Most lay people get very impatient and drift away from this archaic style of expression.
My purpose is not to bore the pants off of you, but to put into modern terms ancient ideas that have been validated over thousands of years. I promise not to do this often, and I hope that my choice here will not be too extended or esoteric for you. These are just fragments, of a much longer works and is only a few of many dealing with the instant topic. All of the following are translated by Professor H.C. Warren.
"He, then, that has no clear idea of death and does not master the fact that death everywhere consists in the dissolution of the Groups (the "Groups" referred to are those elements that make up the "individual")
he comes to a variety of conclusions, such as, "A living entity dies and transmigrates into another body."
He that has no clear idea of rebirth and does not master the fact the appearance of the Groups everywhere constitutes rebirth, he come to a variety of conclusions, such as, "A living entity is born and has obtained a new body."
Yisuddhi-Magga (Chap. Xvii)
Later from the same work,
Here is the Candle analogy as it appeared in the Pali text Milindapauha.
"Said the king, "bhante Nagasena," ("bhante" is a term applied to a venerated and enlightened Master. Nagasena was very early on often quoted and probably was a close disciple of the historical Buddha)
"Does rebirth take place without anything transmigrating?"
"Yes, your majesty. Rebirth takes place without anything transmigrating."
"How, bhante Nagasena, does rebirth take place without anything transmigrating? Give an illustration."
"Suppose, your majesty, a man were to light a light from another light; pray, would the one light have passed over (transmigrated) t the other light?"
"Nay, verily, bhante."
"In exactly the same way, your majesty, does rebirth take place without anything transmigrating."
"Give another illustration."
"Do you remember, your majesty, having learnt, when you were a boy, some verse or other from your professor of poetry?"
"Yes, bhante."
"Pray, your majesty, did the verse pass over (transmigrate) to you from your teacher?"
"Nay, verily, bhante."
"In exactly the same way, your majesty, does rebirth take place without anything transmigrating."
"You are an able man, bhante Nagasena."
Let's not do this again, it's as much a hassle to type in properly as it is for the modern audience to read. For those who really want to know about Buddhism, you will read a lot of this sort of thing. To really do it properly you need to learn at least some Pali and Sanscrit. Imagine trying to study early Christian works without an understanding of Greek, Latin, Hebrew and Aramaic.