Believing things 'on authority' only means believing them because you have been told them by someone you think trustworthy. Ninety-nine percent of the things you believe are believed on authority. I believe there is such a place as New York. I could not prove by abstract reasoning that there is such a place. I believe it because reliable people have told me so.
Every historical statement is believed on authority.
None of us has seen the Norman Conquest or the defeat of the Spanish Armada. His character is trustworthy, faithful, and full of grace. Because God was not required to grant anything to sinful people, His promises and fulfillment of them are simply based on His character. As you journey through life, you will continually be asked to accept and believe God's promises on the basis of His character and authority. They have bowed down and fallen, but we have risen and stood upright.