"Taking Three as the subject to reason about—
A convenient number to state—
We add Seven, and Ten, and then multiply out
By One Thousand diminished by Eight.
"The result we proceed to divide, as you see,
By Nine Hundred and Ninety and Two:
Then subtract Seventeen, and the answer must be
Exactly and perfectly true."
The Butcher's calculation looks like this:
[ (3 + 7 + 10) x (1000-8) ] / 992 - 17 = 3
It is a true calculation, but would have worked as well for any other starting number besides 3 and is therefore not at all relevant to the Beaver's concern about how to add 2 and 1.
Here are links to more nonsense verse by Lewis Carroll and also by Edward Lear.
Langford Reed (1889-1954), a nonsense poet himself, was a collector and editor of nonsense verse. In a Reed collection published by G. P. Putnam's Sons (1926) is found this poem by a poet about whom I've been able to learn nothing more than his name, E. P. Dempster. In the poem below, Dempster has good fun with the sounds and alternative meanings of mathemtical terms:
A Mathematical Madness by E P Dempster
For months I had been "grinding" Mathematics day and night
When Miss McGirton cast on my affections such a blight:
My mind unhinged now only creaks, and when I tell my woes
I'm forced to lisp in numbers what I'd rather say in prose.
Sweet maiden perpendicular! She gave a slanting sigh
As o'er my kneeling form she cast a calculating eye.
"Ah! well," said I, "you cipher me, for if you'll not be mine
From out this pocket next my heart I'll straight produce a line;
So ere you are, dear Polly, gone, pray heed your lover's vow,
Or he dangles at right angles to some horizontal bough."
The maid flew in no frustrum—like your giddy gushing girls—
But standing calm and frigid, shook her strictly spiral curls,
And said, "You see we're equal as to station: very well!
Our paths in life could never meet, because they're parallel."
Her voice was so serrated that I fled this maid antique;
Then, approaching her obliquely, at a tangent took her cheek!
The kiss was too elliptical! She vanished into space!
And a circulating obelisk now marks the fatal place.
Weeks fled. My doctor shook his head and said, "You must embark
For an utter change." I did: and went aboard a leaky Arc
Bound for the hot Quadratics, where I landed for a week,
And joined the aborigines in every savage freak.
I felled primeval forests with the axes of a cube,
At the feathery Parabolas I aimed the loaded tube:
While safe within some brackets I have watched those bulky brutes,
The snorting Parallelograms that feed upon square roots,
Their noise would rouse the forest till each denizen therein
Woke up and did its "level best" to swell the horrid din.
Oh! the shrieking of the Cylinder! the Pyramid's base moan,
The clucking of the Sector and the cooing of the Cone!
And oft, when looking for a log I'd shake in ev'ry joint
For fear some deadly Decimal might sting me with its point.
At last I plucked up courage, though, and even gained renown
In getting gallant trophies for my house in Camden Town:
I trapped the roaring Rhombuses, those beasts of fearful strength,
And the Parallelopipedon, a snake of awful length;
Oft I bestrode the Algebra and charged in wild career
The proud opaque Hypotenuse and jabbed him with my spear.
'Tis past! I'm now in London; yet my reason's all awry.
I'm yearning for a vanished maid who gave a slanting sigh.
Nor may we meet in Dreamland: e'en there I'm robbed of rest,
For a wizened old Trapezium sits sulking on my chest;
On two triangles she jangles with a semilunar leer,
Till I wake—with hair erect—in one diagonal of fear!
And mark to the clang of symbols, phantom figures march all day
In co-efficient cohorts—Major Axis leads the way.
In short, from early morn until I shuffle off to bed,
But one equation's clear to me, — o = ayz.
Note (17 December 2015): -- An anonymous reader has asked about the final equation above. I once suspected that zero was intended instead of oh, but have not been able to verify that. And indeed, as currently written, it satisfies the condition of nonsense. My original source for the poem was this Wikipedia link and today I discover that the poem is no longer there. I have on my shelves a collection of Langford Reed's nonsense verse -- but my collection does not include this poem.