**When X Cubed**by Niccolò Tartaglia (1500–1557) (Englished by Kellie Gutman)

When x cubed’s summed with m times x and then

Set equal to some number, a relation

Is found where r less s will equal n.

Now multiply these terms. This combination

rs will equal m thirds to the third;

This gives us a quadratic situation,

Where r and s involve the same square surd.

Their cube roots must be taken; then subtracting

Them gives you x; your answer’s been inferred.

The second case we’ll set about enacting

Has x cubed on the left side all alone.

The same relationships, the same extracting:

Seek numbers r and s, where the unknown

rs will equal m-on-3 cubed nicely,

And summing r and s gives n, as shown.

Once more the cube roots must be found concisely

Of our two newfound terms, both r and s,

And when we add these roots, there’s x precisely.

The final case is easy to assess:

Look closely at the second case I mention --

It’s so alike that I shall not digress.

These things I’ve quickly found, they’re my invention,

In this year fifteen hundred thirty-four,

While working hard and paying close attention,

Surrounded by canals that lap the shore.

And here is the original Italian version by Tartaglia:

**Quando che’l cubo**

Quando che’l cubo con le cose appresso

Se agguaglia à qualche numero discreto

Trovar dui altri differenti in esso.

Dapoi terrai questo per consueto

Che'l lor produtto sempre sia eguale

Al terzo cubo delle cose neto,

El residuo poi suo generale

Delli lor lati cubi ben sottrati

Varra la tua cosa principale.

In el secondo de cotesti atti

Quando che’l cubo restasse lui solo

Tu osservarai quest'altri contratti,

Del numer farai due tal part’à volo

Che l’una in l’altra si produca schietto

El terzo cubo delle cose in siolo

Delle qual poi, per commun precetto

Torrai li lati cubi insieme gionti

Et cotal somma sara il tuo concetto.

El terzo poi de questi nostri conti

Se solve col secondo se ben guardi

Che per natura son quasi congionti.

Questi trovai, e non con passi tardi

Nel mille cinquecentè, quatro e trenta

Con fondamenti ben sald’è gagliardi

Nella citta dal mar’ intorno centa.

Kellie O. Gutman lives in Boston, Massachusetts. With her husband Richard J.S. Gutman, she has written and published two books. Gutman's translation of "Quando Che'l Cubo" first appeared in

*The Mathematical Intelligencer,*27 (1) 2005, 32-36.

Thank you! I've always wanted to read this in English.

ReplyDeleteI'm grateful to Kellie for the translation. Thanks for dropping by!

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