Formens evige Magie
(Et poetisk Spilfægteri)
Om Kageformen, eller selve Kagen
Er Hovedsagen
I denne Verden, gaae vi her forbi.
Jeg bringer — (ja, det kommer til det samme)
Jeg bringer nemlig her en lille Ramme
Til hvad jeg skrev og kaldte Poesi.
Og muligvis faaer Rammen meest Værdi,
Thi den har „Formens evige Magie”
Og den kan stikke Hjertets Poesi.
Han, som til Dato vragede hvert Stykke,
Jeg bragte frem (fordi deri var Skygge)
Maaskee hos ham min Ramme gjør sin Lykke,
Thi jeg skal trænge den i Formen ind;
Jeg vil den seje Prosa-Lyng oprykke,
Og, kort sagt — lave Suppe paa en Pind.
Hvad der er mest mod Poesien bister,
Geometriens yndede Magister
Matheseos, jeg her paa Bladet rister;
See saa! pas paa Enhver.
Trianglen ABC er givet her,
Retvinklet og paa Siderne Quadrater;
Beviset er nu om de to Krabater,
Det, at Quadraterne paa hvert Catheder
AC, BC (jeg naevne disse Steder)
Er’ just i Eet og Alt, som den Krabat,
Hypothenusen kalder sin Quadrat.
Nu gaae vi da til vore Præparater.
En lodret Linie maa man som De veed
Her drage til den større Side ned,
Og saa forlænge den endnu til K,
Da vil man finde, ei det mindste mangler,
AB-Quadraten ganske rigtig staae
Delt (som AK BK) i to Rectangler.
(Thi tvende Linier, man veed,
Har just det generelle,
Naar paa en tredie de staae lodret’ ned,
Saa er’ de ogsaa ganske paralelle.)
Nu drages en fra A til G, fra C til I,
Og da Præparationen er forbi.
Ei sandt, o Mester! — true dog ei med Riset!
Nu gaae vi til Beviset.
— Vi har de to Triangler ABG
Og CBI, hos dem er Vinklen p
Lig Vinklen o, men o er lig en Ret,
Ja, der er Ingen, som vil nægte det
Thi rette Vinkler er der i Quadrater,
Nu Vinklen r lig Vinklen r. Ei sandt?
(Thi sund Fornuft kan sige
Hver størrelse jo med sig selv er lige.)
Saaledes p plus r lig o plus r man fandt,
(Her i Figuren staae de smaa Krabater.)
Naar lige nu til begge bliver lagt,
En lige Sum er da tilvejebragt.
(Nu er vi med Beviset snart forbi,
Det stærkt mod Enden lider.)
See Vinklen ABG lig CBI,
AB er lig BI, BG er lig BC
(I en Quadrat er’ lige store Sider,
Derfor, saasandt som Tre gjør altid Tre,
To Sider og en Vinkel vil os lette),
Trianglen ABG vi her tør sætte
Lig CBI (og det er intet Træf),
Nu ABG er lig en halv BF
Pas paa!
Nu CBI er lig en halv BK.
(Husk: lige stort for lige stort kan gaae.)
Eens er Divisor, eens er Dividenden;
Eens bliver altsaa ogsaa Quotienten,
Og ad den samme Vei vi faae:
AD er lig AK.
Der har Du Maaden,
Snart som Pythagoras man løser Gaaden.
Ja løst, beviist — Du store Trylleri!
Du Himmel Tak! — at det er nu forbi!
Thi slige Vers er ikke Narreri;
De løbe vel, som der var Intet i —
Dog her var jo Fornuft og Form-Magi.
Det sidste vil jeg haabe,
Og denne Form er i det mindste fri
For hvad der dæmper slemt hver Melodi:
En Mudderdraabe.)
Fornuft og Form har her skabt — Poesi.
Her seer man „Formens evige Magie.
Form’s endless Wizardry
(Sheer poetical posturing)
Whether the cake tin or the actual cake
Is what’s at stake
Here in this world, I’ll leave for you to see.
I have with me – (it’s more or less the same)
I have with me what is a small-sized frame
For what I wrote and called it poetry.
The frame perhaps has greater potency
For it has ‘Form’s eternal wizardry’,
Which overtrumps with ease heart’s poetry.
He who to date did every piece reject
That I brought forward (shadow is suspect)
Perhaps my frame he gladly will recruit,
For in the form I’ll cram it without fail;
I’ll tear all heather-prose up by the root
And, to be brief, I’ll make soup from a nail.
What is to poetry a real disaster,
Geometry’s revered and cherished Master
Matheseos, I on the page inscribe
Right, then! Take care should you wish to imbibe.
What’s given here’s an ABC triangle,
Squares on its sides, all at right angles
What now has to be proved for these two culprits
Is that the square of them on both the pulpits
AC, BC (I name them as a pair)
In every way is equal to the square
Of the hypothenuse, the final culprit.
So let’s consult our models to resolve it.
A line plumb vertical, as you well know,
One draws down to the long side at one go,
Then it’s extended all the way to K,
This done one finds, with nothing at all lacking,
The square of AB standing as it should
With AK, BK as its two rectangles
(A brace of two straight lines, although unplanned.
Possess a feature that is general,
When on a third they vertically stand
They also are completely parallel.)
Now one is drawn from A to G, from C to I,
And then the demonstration meets the eye.
Not so, oh master! Put away your cane!
The proof will make this plain.
– We have the two triangles ABG
Andf CBI, which have the angle p
That equals o, but o is straight and right
Yes, there is no one who this would deny.
Because there are right angles in a square,
Now angle r’s as angle r, aren’t they a pair?
(For common sense would make this sequel
That every unit with itself is equal.)
Thus p plus r as o plus r must be.
(Here in the figure the small culprits are)
When something equal to them both is laid,
An equal sum is always thereby made.
(And now our proof is almost Q.E.D.,
The end is now in sight, as you will see.)
CBI and ABG are equal
So too AB BI, BG BC
(In a square all sides are always equal,
Just as three’s always the same as three,
Two sides and an angle helps us greatly),
Here we claim the triangle ABG
Equals CBI (and not by chance)
Now ABG is just half of BF
Take care!
Now CBI is just half of BK.
(NB. Equal for equal always can apply.)
Divisor equals here the dividend,
And so the quotient is right at the end,
And using the same method we can say:
AD equals AK.
The method’s trouble-free
Quick as Pythagoras it’s Q.E.D.
Yes, solved and proved – what wizardry indeed!
Thank heavens! that no further proof we need!
The verses here are no tomfoolery;
They run along as smoothly as can be –
But here was reason and form-wizardry.
(Just one last thing I hope before I stop,
And this form is at least completely free,
For what can badly clog each melody:
Some mud – a single drop.)
Reason and form have made here – poetry.
Here can one see ‘Form’s endless wizardry’.
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