More hitherto untraced quotations/allusions in the Biographia. Apologies; but I need to park all the instances of this sort of thing I discover for future reference. The first is an especially dull one, too. Bear with me.
Editors have traced the Miltonic use, not least because Coleridge quotes the passage he means (from Paradise Lost) at the bottom of this very paragraph. But they haven't traced the Hooker or Sanderson; Engell and Jackson Bate in fact assert that they think Sanderson doesn't use 'intuition' ('no particular example of the use of intuition has been found in the works of Bishop Sanderson'). They're wrong, though.
Take them one at a time. Richard Hooker is much concerned with what he calls the fullest development of faith, ‘the intuitive vision of God in the world to come’ [Of the Lawes of Ecclesiastical Politie 1 (1594): 12:11]. And English theologian Robert Sanderson (1587-1663) talks in his The Case Determined: of the Military Life (1678) of ‘the intuition of Honour and Glory’ as a ‘lawful and commendable’ thing in a soldier. [The Works of Robert Sanderson (ed William Jacobson; 6 vols 1854), 5:112]. For completeness's sake, here's the bit in Paradise Lost (5:487-9) where the angel Raphael explains to Adam that ‘reason’ is either ‘Discursive, or Intuitive’, adding that ‘discourse/Is oftest yours, the latter most is ours.’ The distinction is one of immediacy of apprehension of truth (‘Discursive or Intuitive—, Tracing Truth from Argument to Argument, Discerning, Examining, Distingushing, Comparing, Inferring, Concluding. This is Discourse; whether with One Another, or Alone; whether in Words or Mentally. Intuitive is when the Mind Instantly perceives Truth as we with one Glance of the Eye Know if the Object is Red, Green, White etc.'[Jonathan Richardson, Explanatory Notes and Remarks on Milton's Paradise Lost (1734), 229].
The second one, though, is just smallbeer. In chapter 10 Coleridge recalls living at Nether Stowey, during the invasion panic of the Napoleonic Wars, when he and Wordsworth were suspected of being French spies. 'Far different were the days to which these anecdotes have carried me back. The dark guesses of some zealous Quidnunc met with so congenial a soil in the grave alarm of a titled Dogberry of our neighbourhood.' Engell and Bate gloss 'Quidnunc' thus: 'literally "what now?" Hence an inquisitive, gossipy person' [BL 1:193]. That's not right. In fact Quidnunc is the title character in the once-popular play, The Farce of the Upholsterer (1758) by Arthur Murphy. Young Bell loves Quidnunc’s beautiful daughter, but his way is blocked: ‘the Man’s distracted about the Balance of Power and will give his Daughter to none but a Politician.— … his Head runs upon Ways and Means, and Schemes for paying off the national Debt: The Affairs of Europe engross all his Attention, while the Distresses of his lovely Daughter pass unnoticed’ [Murphy, The Upholsterer, a Farce in Two Acts As it is Performed at the Theatre Royal in Covent-Garden (1763), 6]. Dogberry, of course, is the incompetent but self-satisfied night constable from Shakespeare’s Much Ado About Nothing.