MacTutor
The Moving Finger writes; and, having writ,
Moves on : nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
Myself when young did eagerly frequent
Doctor and Saint, and heard great Argument
About it and about: but evermore
Came out by the same door as in I went.
Khayyam, who stitched the tents of science,
Has fallen in grief's furnace and been suddenly burned;
The shears of Fate have cut the tent ropes of his life,
And the broker of Hope has sold him for nothing!'
[His name means a tent maker.]
For in and out, above, about, below,
'Tis nothing but a Magic Shadow-show,
Played in a Box whose Candle is the Sun,
Round which we Phantom Figures come and go.
Ah, but my Computations, People say,
Have Squared the Year to human Compass, eh?
If so, by striking from the Calendar
Unborn Tomorrow, and dead Yesterday.
By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible. Such a thing is either a quantity or a unique rlation, which is only determined by careful examination. What one seaches for in the algebraic art are the relations which lead from the known to the unknown, to discover which is the object of Algebra as stated above. The perfection of this art consists in knowledge of the scientific method by which one determines numerical and geometric unknowns.
I was unable to devote myself to the learning of this algebra and the continued concentration upon it, because of obstacles in the vagaries of time which hindered me; for we have been deprived of all the people of knowledge save for a group, small in number, with many troubles, whose concern in life is to snatch the opportunity, when time is asleep, to devote themselves meanwhile to the investigation and perfection of a science; for the majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes; and if they see a certain person seeking for the right and preferring the truth, doing his best to refute the false and untrue and leaving aside hypocrisy and deceit, they make a fool of him and mock him.
Algebras are geometric facts which are proved.