18794
[Commentary:
The problem on this page is from Propositions 12 and 14 from Effectionum geometricarum canonica recensio
(Viète 1593b, Props 12, . Harriot does not mention the Effectionum explicitly here but the notation is essentially Viète's, except reduced to lower case letters.
Note Harriot's use of the symbol for what we now write as .
Note also that once he has arrived at an equation, he regards the problem as solved. The rest is merely 'mechanicen', or practical calculation.
Harriot's source for the method of Diophantus must have been the edition of Wilhelm Diophanti Alexandrini rerum arithmeticarum libri sex (Diophantus . Mahomet was by now all that was remembered of the name of Muhammad ibn Musa al-Khwarizmi. His name appears in this form in Bombelli's Algebra (Bombelli 1572, , for example. ]
Note Harriot's use of the symbol for what we now write as .
Note also that once he has arrived at an equation, he regards the problem as solved. The rest is merely 'mechanicen', or practical calculation.
Harriot's source for the method of Diophantus must have been the edition of Wilhelm Diophanti Alexandrini rerum arithmeticarum libri sex (Diophantus . Mahomet was by now all that was remembered of the name of Muhammad ibn Musa al-Khwarizmi. His name appears in this form in Bombelli's Algebra (Bombelli 1572, , for example. ]
Data media trium proportionalium et differentia extremarum:
invenire
[Translation: Given the mean of three proportionals and thd difference of the extremes, find the ]
invenire
[Translation: Given the mean of three proportionals and thd difference of the extremes, find the ]
Sit media data . et differentia .
Et ponatur unus terminus ignotus .
Ergo alter erit . hoc est
vel vel .
Ergo: Resolutio.
Ergo per Mechanicen.
Hoc est Minor.
[Translation: Let the given mean be and the difference , and denote one of the unkonwn extrmes by .
Therefore the other will be , that is, either a + b
Hence the solution.
Therefore by calculation
That is, the lesser extreme
the ]
Et ponatur unus terminus ignotus .
Ergo alter erit . hoc est
vel vel .
Ergo: Resolutio.
Ergo per Mechanicen.
Hoc est Minor.
[Translation: Let the given mean be and the difference , and denote one of the unkonwn extrmes by .
Therefore the other will be , that is, either a + b
Hence the solution.
Therefore by calculation
That is, the lesser extreme
the ]
Et emitandas applicationes in fine mechanicas, melius est
ponere vel notare in principio, dimidium differentiæ . tum differentia
tota erit .
Ergo per resolutionem
solutio fit
Ergo per
[Translation: To force out the divisions in the final calculation, it is better to put or denote from the beginning half the difference , then the total difference will be . Hence from the solution, the equation will be.
Therefore by ]
ponere vel notare in principio, dimidium differentiæ . tum differentia
tota erit .
Ergo per resolutionem
solutio fit
Ergo per
[Translation: To force out the divisions in the final calculation, it is better to put or denote from the beginning half the difference , then the total difference will be . Hence from the solution, the equation will be.
Therefore by ]
Mechanicum secundum Diophantum
et Mahometen.
Adde utrique parte æquationis .
[…]
Et per
[Translation: Calculation according to Diohantus and Mahomet.
Add to each side of the equation.
And by ]
et Mahometen.
Adde utrique parte æquationis .
[…]
Et per
[Translation: Calculation according to Diohantus and Mahomet.
Add to each side of the equation.
And by ]