A hypothetical instrument or tool for measuring aspects of a diagram; a specialist in measuring diagrammatic properties.
From diagram plus -meter (from Greek metron meaning 'measure'). This appears to be a constructed or theoretical term not in standard dictionaries.
Like 'thermometer' measures temperature and 'barometer' measures pressure, a 'diagrammeter' would theoretically measure... diagrams? This shows how the -meter suffix is so productive that English speakers instinctively understand words they've never heard, creating meaning from component parts.
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