Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
--
As quoted in "A Paper of Omar Khayyam" by A.R. Amir-Moez in Scripta Mathematica 26 (1963). This quotation has often been abridged in various ways, usually ending with "Algebras are geometric facts which are proved", thus altering the context significantly.Omar Khayyam
All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole.
Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra.
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.Benjamin Peirce
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 relation, which is only determined by careful examination. What one searches 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.
Omar Khayyam
Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.
Fran Lebowitz
The elements of justice are identical with those of algebra.
Pierre-Joseph (P. J.) Proudhon
That night Paradine slept badly. Holloway's parallel had been ill-chosen. It led to disturbing theories. The x factor — The children were using the equivalent of algebraic reasoning, while adults used geometry.
Fair enough. Only —
Algebra can give you answers that geometry cannot, since there are certain terms and symbols which cannot be expressed geometrically. Suppose x logic showed conclusions inconceivable to an adult mind?Lewis Padgett
Khayyam, Omar
Khomeini, Ruhollah
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z