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LIST OF WORKS

WHICH HAVE BEEN REFERRED TO BY INITIAL LETTERS,

Leg.

W.

Wood, Algebra. E.

Euler, Algebra. E. Add. Additions in the second edition of Euler's Algebra. F.

Francour, Cours complète de Mathematiques pures. Bour. Bourdon, Algèbre. L.

Lacroix, Eléments d'Algèbre. L. C.

Lacroix, Compléments d'Algèbre. B.

Barlow, Theory of Numbers. Leg.

Legendre, Théorie des Nombres. G.

Garnier, Eléments d'Algèbre. G. A. Garnier, Analyse Algèbrique. E. M. Encyclopedia Metropolitana.

(In Trigonometry.) Legendre, Trigonométrie. W.

Woodhouse, Trigonometry. L.

Lardner, Trigonometry.
C.

Cagnoli, Trigonométrie.
Biot, Biot, Essai de Géométrie Analytique.
G. G. A. Garnier, Géométrie Analytique.
H. A. G. Hamilton, Analytical Geometry.
H. C. S. Hamilton, Conic Sections.
L. A. G. Lardner, Algebraic Geometry.
Hust.

Hustler, Conic Sections.
L. C. D. Lacroix, Traité du Calcul Differentiel, &c.
L. D. C. Lardner, Differential Calculus.
Tr. L. Translation of Lacroix, Differential Calculus.
L. Mec. Cel. Laplace, Mécanique Céleste.

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267 last

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ALGEBRA.

Art. (1.) Definitions and Axioms.

(W.47—72; &c.)

(2.) Rules for addition, and subtraction.

a +(6c)=a+b-c.
a-(6-c)=a-b+c.
a +(-c)=a-C.
a-(-C)=a+c.

(3.) Rules for multiplication and division,

(ab)c=ac-bc.
(a - b)(c-d)=ac-bc- ad + bd.
(a - b)(-d)= -ad + bd.
(-6)(-d)=bd.

(F.947.) The general rule for the signs both in multiplication, and division is, that like signs give a positive, and unlike, a negative, result.

(4.) a"=a.a.a...... to n factors.

am xa" =am+n. (1)
(a")" =amn

If n is not a positive integer, the signification of an is conventional, being merely such as to satisfy equation (1).

am-n=ama".
a=am-m=1.

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