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[Commentary:
This page refers to Euclid X.37. In modern editions the relevant proposition , but Harriot's numbering matches that of both Commandino and Clavius.
If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be called binomial.
Harriot's example is .
There is also a reference below the diagram to Euclid, .
Triangles and parallelograms which are under the same height are to one another as their bases. ]
If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be called binomial.
Harriot's example is .
There is also a reference below the diagram to Euclid, .
Triangles and parallelograms which are under the same height are to one another as their bases. ]
Lib, 10: prop.
[Translation: Book X, Proposition ]
[Translation: Book X, Proposition ]
Si duae rationales potentia solum commensurabiles componantur,
tota irrationalis erit, nocetur autem ex binis
[Translation: If two quantities commensurable in power only are combined, the whole will be irrational, moreover separated into two parts.
tota irrationalis erit, nocetur autem ex binis
[Translation: If two quantities commensurable in power only are combined, the whole will be irrational, moreover separated into two parts.