Biography is Greek in both halves — bios, "life," plus graphia, "record, account" — but it is not an ancient Greek word. Classical Greek just said bios. The compound biographia turns up only in later Greek, and English took it in the 1680s through Medieval Latin. That is the usual pattern for scholarly-looking Greek vocabulary: the parts are genuinely ancient, the assembly is modern, and the spelling tells you about the parts rather than about any continuous history.
The -graphy ending has since become one of the most productive word-building tools in English, giving geography, photography, calligraphy and hundreds more. Biography itself started as the name of a branch of literature and only narrowed to "a history of one person's life" in 1791. English has never settled on a verb: biographise, biography and biograph were all tried in the 1800s and all quietly died.
biography (n.) 1680s, "the histories of individual lives, as a branch of literature," probably from Medieval Latin biographia , from later Greek biographia "description of life" (which was not in classical Greek, bios alone being the word there for it), from Greek bios "life" (from PIE root *gwei- "to live") + graphia "record, account" (see -graphy ). The meaning "a history of some one person's life" is from 1791. The meaning "life course of any living being" is by 1854. No one-word verb form has become common; biographise / biographize (1800), biography (1844), biograph (1849) have been tried. also from 1680s
biography came in through Greek, and its spelling follows that family's conventions.
How that family writes these sounds
| a technical compound you could take apart | the combining forms: auto-, bio-, micro-, tele-, -logy, -graph, -meter, -scopebiography, microscope, telemetry |
What gives it away on the page
| auto-, bio-, micro-, tele-, -logy, -graph, -meter, -scope, -phobia | Combining forms, still productive today.biography, telemetry, microscope |