The title page says it straight out — translated out of "Douche and Latyn" into English, which is to say German and Latin, not Hebrew. Coverdale never pretended otherwise. He wasn't a Hebrew scholar; he worked from Luther and the Zurich men and the Vulgate, and leaned hard on Tyndale wherever Tyndale had got there first, which was most of the New Testament and a long stretch of the Old. The blackletter on that woodcut page is handsome, Adam and Eve up one side, a king enthroned at the foot, and the date sitting there in roman numerals: 1535. Printed abroad. The editions actually printed in England came two years later, and the folio of those carried the royal licence.
What he had instead of the languages was an ear. A good many phrases people use without any idea where they picked them up came out of his desk — "loving kindness" is his, as near as anyone can tell, and the plainer bits of the psalms have his rhythm all through them. His Psalter went into the Great Bible of 1540, then into the Book of Common Prayer from 1662, and stayed in the American Episcopal books until 1979. Four hundred years of people saying his sentences aloud on Sunday mornings, mostly not knowing his name.
I have two prayer books on the shelf behind me. One is clean and tight and nobody has ever opened it; the other falls open at the psalms on its own, the spine gone soft there, a thumbprint on the page.
That title page is usually given to Holbein the younger, Jun, though what you actually hold in your hand is the work of whoever cut the block — the lines in the border are a knife's lines, not a pen's. Nobody wrote his name down.