Meaning of the phrase "if i may so say" in Newtons writing

I have been trying to read through Newton's Principia and this phase has come up several times so far, usually in the context of a mathematical operation. I cannot see any additional information or purpose in this phrase bring added, but it happens repeatedly. Did this phrase have a real purpose in the writing or is it just an artifact of the attempted direct translation from Latin?

Law III:[...] If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone -- Page 83

These things being done, we are to take the product (if I may so say) of the body A, by the chord of the arc, TA (which represents its velocity), that we may have its motion in the place A immediately before reflexion -- Page 91

Solution 1:

This is a translation of a insertion that Newton made after the printing of the first edition. It is present in the second edition. You can see on the Cambridge facsimile, Newton has inserted the Latin phrase "ut ita dicam" in handwriting. This has been faithfully reproduced in the second edition.

This Latin phrase is discussed by an article which:

argues that its function is pragmatic in essence, since it operates both as a discourse marker, namely an interpretative device favoring the cooperative construction of the contextual meaning, and as a pragmatic marker capable of modulating the force of a potentially face-threatening statement or the employment of a daring term.

The function of this phrase is to engage the reader and ask them to cooperate with the writer and consider a potentially difficult concept (that the stone pulls on the horse)

"Ut ita dicam" may be translated as "So I say". "Ut ita" is a conjunction, roughly "so" and dicam is the first person singular subjective form of "dico: I say"

Solution 2:

I understand, if I may say so. That is the modern formatting of that phrase, to use an expression in an unusual way, and to declare that you're doing it. We could say "in a manner of speaking," or simply "if I can say it that way."

To pick it apart a bit,

the plane is held, if you will indulge me in what I do say to illustrate this ('if I may so' say) in the air by the negative air pressure created by the shape of its wings moving through the air.