Trying to keep away from religion but, making note that many religions believe in reincarnation. Judeo-Christian believed as well as Zoroastrianism, Buddhism, Hinduism, Taoism, and so on. Though all Christians do not, there are some that believe reincarnation is the way into heaven. Each life strives to be more perfect than the last until they reach a perfect spirit. At that point the cycle ends and they enter into the kingdom of heaven.
There are a few quotes in the bible that are used to "prove" reincarnation but, I think they are taken out of text and would never use them to "prove" it. My views of the Holy Bible are that if one's beliefs are such and such, they will find "proof" in the scriptures to back it up but, that is another whole ball of wax and not here or there at the moment.
There are also a few quotes in the bible that are used to "disprove" reincarnation. My favorite is "man dies once and is then judged". So, to avoid argument it would be better not to use these as "proof".
My proof is my own personal experiences with past lives. Others have had "their" experiences be it through memories, reverie, hypnotism or other conveyances. Some even believe dejevue to be past life experience and maybe it is, I don't know.
I have learned that some things "trigger" past lives automatically in me. I have had moments where just staring into a campfire or the flickering of light through rows of trees in a forest was enough to awaken a past life. However, one finds it, if he wants it, he will discover it on his own.
Ernest