In the passage from Newman that I included in my last post, the great divine, philosopher, and man of letters makes the following comment about ‘scientific’ as opposed to ‘poetic knowledge’:
Its mission is to destroy ignorance, doubt, surmise, suspense, illusions, fears, deceits, according to the ‘Felix qui potuit rerum cognoscere causas’ of the Poet, whose whole passage, by the way, may be taken as drawing out the contrast between the poetical and the scientific. 
As I reread this passage last week, the first thing I did was track down the ‘Poet’ whom Newman cites. The line, Felix qui potuit rerum cognoscere causas, as it turns out, is from Book II of Virgil’s Georgics, line 490. In a footnote to the comment about the Poet’s ‘whole passage’, Newman quotes ll. 475, 477, 483-5, 490, and 493. I shall give the ‘whole passage’, including the unquoted lines, according to David Ferry’s translation into English pentameter:
But as for me, oh may the gracious Muses,Gracious beyond all else, whose holy emblemsI consecrated bear in the procession,Grant me their favor and reveal to meThe courses of the stars above in the heavens;Teach me about the sun in its eclipse,And about the many labors of the moon;What is it that causes quakings of the earth?What force is it that suddenly makes the greatSea rise and swell and break through all restraintsAnd then subside into itself again?Why is it that the sun in winter hurriesTo plunge itself into the sea and whyIs the winternight so slow to come to an end?But if the blood around my heart’s too coldTo gain me access to such mighty knowledge,Then may I find delight in the rural fieldsAnd the little brooks that make their way through valleys,And in obscurity love the woods and rivers.I long for such places, oh I long to beBy Spercheus or at Taygeta in SpartaWhere maidens celebrate the rites of Bacchus,Or to be safe in the cool Haemian glade,Protected in the shade of those great branches!
That man is blessed who has learned the causes of things,And therefore under his feet subjugates fearAnd the decrees of unrelenting fateAnd the noise of Acheron’s insatiable waters.He too is happy who knows the country gods,The sister Nymphs, and Pan, and old Sylvanus. 
I take it that Newman is suggesting that the poet’s ‘fear’ before ‘such mighty knowledge’ corresponds to the poetic mode, whereas the desire to learn ‘the causes of things’ represents the scientific mode of knowledge. I am less certain what to make of where Newman would say the poet’s affinity for the still natural but tamer, ‘obscurity’ of fields, valleys, woods, and rivers fits into the scientific/poetic dichotomy. Are these more ‘scientific’ because less ‘vast, immeasurable, impenetrable, inscrutable, mysterious’ than the heavens or the ocean? And the country gods’ place in this scheme is still more puzzling to me. But perhaps that is for another post.
In the meantime, I came across another poem, of a much lower order than Virgil’s, which nevertheless constitutes an apt illustration of the distinction between scientific and poetic knowledge. Here is Walt Whitman’s, ‘When I Heard the Learn’d Astronomer’, which I only just now discovered was recited on the popular television programme, Breaking Bad:
When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars. 
 John Henry Newman, Rise & Progress of Universities and Benedictine Essays, Vol. 3 of The Works of Cardinal John Henry Newman, Birmingham Oratory, Millennium Edition (Notre Dame, IN: U of Notre Dame, 2001), pp. 386-7.
 David Ferry, tr., The Georgics of Virgil: Bilingual Edition (NY: Farrar, 2006), p. 85.
 Walt Whitman, Leaves of Grass (NY: Barnes & Noble, 1993), p. 228.