True to the line.
In 1825, George Washington Doane, Bishop of New Jersey, wrote a poem entitled What Is That, Mother?, which included this verse:
What is that, Mother? The eagle, boy! Proudly careering his course of joy, Firm, on his own mountain vigour, relying, Breasting the dark storm, the red bolt defying, His wing on the wind, and his eye on the sun, He swerves not a hair, but bears onward, right on: Boy, may the eagle's flight ever be thine, Onward, and upward, and true to the line.
By 1829, the poem had reached the London Literary Gazette, and by the mid 1830s, was becoming manifold in books for schoolchildren learning to read. It is possible that several generations of children individually read aloud the phrase “onward and upward” in its poetic context.
The extract “Onward and upward and true to the line” can be found in would-be inspirational speeches and sermons of the mid-to late 1800s, no doubt confident that listeners would have the heroic eagle vision emblazoned upon their minds as they heard it.
In the context of preaching, the poem’s scene would have evoked the well-known Isaiah scripture: soaring on eagle’s wings, running without tiring, walking without weakening, and it is not hard to see how “onward and upward” could have taken on a life of its own as a motto for those wanting to motivate themselves and/or others to press on toward higher things.
Quora.com Mark Christian-Edwards, MA from Durham University (2018)