What Jacobus (aka Jacob aka James) Arminius believed and taught is not precisely the same thing as what became Arminianism, but it allowed for it and produced it.
There it is: Arminius himself may not have said it, but he provided for it to be said, as:
"Although human nature was seriously affected by the fall, man has not been left in a state of total spiritual helplessness. God graciously enables every sinner to repent and believe, but He does not interfere with man's freedom. Each sinner possesses a free will, and his eternal destiny depends on how he uses it. Man's freedom consists of his ability to choose good over evil in spiritual matters; his will is not enslaved to his sinful nature. The sinner has the power to either cooperate with God's Spirit and be regenerated or resist God's grace and perish. The lost sinner needs the Spirit's assistance, but he does not have to be regenerated by the Spirit before he can believe, for faith is man's act and precedes the new birth. Faith is the sinner's gift to God; it is man's contribution to salvation." --In which, a person's eternal destiny hinges on his choice and not God's. "Faith is the sinner's gift to God; it is man's contribution to salvation." --either Arminius agrees with this abomination, or Arminianism contradicts Arminius.
Calvinism and Arminianism comparison