Robert Recorde

Robert Recorde is significant as the first British mathematician of any note, and was probably the first to write
in English. He was born in Tenby, Wales in 1510.

Recorde studied at both Oxford University, where he gained a B.A. in 1525 and in 1531 was elected Fellow
of All Souls College, Oxford. He also gained an M.D. from Cambridge University in 1545. He taught
mathematics privately at both universities. He was subsequently appointed as physician to King Edward VI
and Queen Mary. In 1549 he became the first Comptroller of the British Mint and in 1551 was appointed the
General Surveyor of Mines and Monies in Ireland.

Recorde wrote at least five mathematics textbooks, all (except
The Pathewaie to Knowledge) written in the
form of dialogues between teacher and student:
The Grovnd of Artes published in 1543 was a work on arithmetic with applications to commerce,
specifically whole numbers (using computation by abacus and algorism) and fractions. He adopted the - sign
for deficiency and the + sign for excess and described them as follows: '+ whyche betokeneth too muche, as
this line - plaine without a crosse line betokeneth too little.'
A second expanded edition was published in 1552 to include rational numbers as well as whole numbers.
The Castle of Knowledge published in 1551 was a work on astronomy which was an introduction to
Ptolemy’s version of astronomy and also described the Copernican system, although Recorde did not
commit himself to this theory because of fear of being charged with heresy.
The Pathewaie to Knowledge, which was also published in 1551, is a summary of Euclid’s Elements .It was
the first geometry work written in English.
The Whetstone of Witte, published in 1557, is his most famous work on algebra. This includes the
extraction of roots, surds, the use of the German cossic notation for algebraic symbols (which he referred to
as ‘the cossike practise’), and rules for solving equations. It also contains the first use of the = symbol.
Recorde’s reason for adopting the symbol using two lines equal in length was ‘bicause noe 2 thynges can be
moare equalle’.

The title of the book is a play on the words ‘cossike’ and  ‘cos’ which  is the Latin word for whetstone, so the
title of the book could be interpreted as ‘algebra on which to sharpen the wit of mathematics’.

He also introduced the word zenzizenzizenzike to the English language. It is derived from the German word
zenzic, which was an old German word for square, and means the eighth power of a number Recorde
described it as follows: ‘It doeth represent the square of squares squaredly’. The anglicised form of the word,
zenzizenzizenzic, is the only word in the English language with six z’s.

Recorde also wrote one book on medicine entitled
The Urinal of Physick (published in 1547).

Recorde was imprisoned in Southwark, London in 1557 after an altercation with The Earl of Pembroke to
whom he either refused to pay or was unable to pay a £1,000 fine. He died in prison in1558.

A contribution of Recorde to mathematics

A popular problem in Recorde’s time was to calculate how many men should be in the front line of square
batteries of pike-men. It naturally involved finding the square root of the total number of men in the battery.

One particular problem in
The Whetstone of Witte gives three armies: the first army has 5,625 men, the
second has 9,216 men and the third has 15,929 men. The number of men in the front line of each is found
by taking the square roots:
First army: The square root of 5,625 = 75
Second army: The square root of 9,216 = 96
Third army: The square root of 15,129 = 123
But if the three armies were combined, then what would be the number in the front line then?
Add the three numbers together:
5,625 + 9,216 + 15,129 = 29,970
And, the square root of 29,970 = 173 to the nearest whole number.

A related problem goes as follows:
When the army commander arranges his men into a square battery there are 284 men left over. If the
frontline was increased by 1, then there were 25 men too few to complete the square. How many soldiers
were there?

Solution in modern notation

Let the number in the frontline in the first arrangement be x
So the total number of men = x^2 + 284

In the second arrangement, there is a square of side (x + 1) and the total number of men
= (x + 1)^2 - 25

But these numbers must be equal.

Thus (x + 1)^2 - 25 = x^2 + 284
x^2 + 2x + 1 - 25 = x^2 + 284
2x - 24 = 284
2x = 308
x = 154

So the total number of men = 154^2 + 284 = 23,716 + 284 = 24,000