280

HISTORY OF ALGEBRA.

TRACT 33.

is in folio, and intitled Artis Analytics Praxis, ad A : qua-tiones Algcbraicas nova, expedita, SC generali methodo, resol-vendas; a work in all parts of it showing marks of greatgenius and originality, and is the first instance of the modernform of Algebra, in which it has ever since appeared. Itis prefaced by 18 definitions, which are these: 1st, LogisticaSpeciosa ; 2d, Equation ; 3d, Synthesis ; 4, Analysis ; 5,Composition and Resolution ; 6, Forming an Equation ; 1,Reduction of an Equation ; 8, Verification ; 9, Numerosa& Speciosa; 10, Excogitata; 11, Resolution; 12, Roots;13 and 14, The kinds and generation of equations by multi-plication, from binomial roots or factors, called originalequations.

a

b

= aa + ba

a

—

c

— ca —

be,

•a

-f

b

= aaa + baabca

a

+

c

+ caa —

bda

a

d

— da a —

eda

when he puts a for the unknown quantity, and the smallconsonants, b, c, d, See, for its literal values or roots; IS,The first form of canonical equations, which are derivedfrom the above originals, by transposing the homogeneum,or absolute term,

thus aa + ba

— ca = + be, 8tc.

16, The secondary canonicals, formed from the primary byexpelling the 2d term,

thus aa = + bb,or aaa — bba

— bca

— cca = + bbc

+ bee.

17, That these are called canonicals, because they areadapted to canons or rules for finding the numeral roots, &c,

18, Reciprocal equations, in which the homogeneum is theproduct of the coefficients of the other terms, and the firstterm, or highest power of the root, is equal to the product ofthe powers in the other terms, as aaa — caa -f bba — + bbc