Margaret Cavendish (1623-73) -- The Circle of the Brain cannot be Squared

Margaret Cavendish (1623-73) was a writer who published under her own name at a time when most women published anonymously.  Her writing addressed a number of topics, including gender equity and scientific method.
Her romance, The Blazing World, is one of the earliest examples of science fiction. Cavendish was an aristocrat and married William Cavendish to become Duchess of Newcastle-upon-Tyne.  She was so outspoken that William Pepys called her "mad, conceited and ridiculous."
Cavendish wrote Poems and Fancies about science; here is one brief science-sample followed by two with mathematical themes, "The Arithmetic of Passions," and "The Circle of the Brain cannot be Squared."

The weight of Atomes.

If Atomes are as small, as small can bee,
They must in quantity of Matter all agree:
And if consisting Matter of the same (be right,)
Then every Atome must weigh just alike.
Thus Quantity, Quality and Weight, all
Together meets in every Atome small.

These mathematical poems and others by Margaret Cavendish are found on the site Women Scientists in History.

The Arithmetic of Passions

With Numeration Moralists begin
Upon the Passions, putting Quotients in;
Numbers divide with Figures, and Subtract,
And in their Definitions are exact;
As for Subtracting, take but one from three,
Add it to four, and it makes five to be:
Thus the odd Numbers to the even joyned,
Will make the Passions rise within the mind.


The Circle of the Brain cannot be Squared

A Circle round divided in four parts
Hath been great Study 'mongst the men of Arts;
Since Archimed's or Euclid's time, each Brain
Hath on a Line been stretched, yet all in Vain;
And every Thought hath been a Figure set,
Doubts Cyphers were, Hopes as Triangles met;
There was Division and Subtraction made,
And Lines drawn out, and Points exactly laid,
But none hath yet by Demonstration found
The way, by which to Square a Circle round:
For while the Brain is round, no Square will be,
While Thoughts divide, no Figures will agree.
And others did upon the same account,
Doubling the Cube to a great number mount;
But some the Triangles did cut so small,
Till into equal Atoms they did fall:
For such is Man's curiosity and mind,
To seek for that, which is hardest to find.