Harriot, Thomas - Mss. 6785

409205

[Commentary:

The reference at the top of this page is to Zetetic IV.1 from Zeteticorum libri quinque (Viète 1593a, Zet .
Zeteticum I
Invenire numero duo quadrata, aequalia dato
To find in numbers, two squares equal to a given
Harriot's pagination indicates that this page follows Add MS f. , but now

c

and

d

have been replaced by

s

and

r

.
In the second half of the page, Harriot addresses the problem posed in Zeteticum IV.1: to divide a square into two other squares. This is also Problem II.8 in the Arithmetica of Diophantus (Diophantus 1575, . Viète referred to the working by Diophantus, but Harriot refers only to Viète.
Following Viète, Harriot denoted the side of the given square by

b

, the side of the first unknown square by

a

, and the side of the other by

b - \frac{s a}{r}

. The side of the second square is thus found to be

\frac{b r r - b s s}{r r + s s}

. In the 1591 edition of Viète's Zetetica, there is a switch between

R

and

S

at this point, so that the second side is given as

\frac{S^{2} B - R^{2} B}{S^{2} + R^{2}}

. This is the error Harriot refers to. It was corrected in the 1646 edition of Viète's collected works, the Opera mathematica (Viète . ]

2.) Zet. lib. 4.
[Translation: Zetetica, Book IV, Zeteticum ]

Dividere

b b

in
[Translation: To divide

b b

into two [squares]. ]

latus 2i
[Translation: the side of the second square

Contra Vieta, igitur emendandus
vide chartam
[Translation: Contrary to Viete, therefore to be amended
see sheet ]
[Commentary: Sheet 3 is Add MS f. .

221 (111)	222 (111v)
223 (112)	224 (112v)
225 (113)	226 (113v)
227 (114)	228 (114v)
229 (115)	230 (115v)

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