HARRIOT, T.(1560-1621) and OUGHTRED, W.(1574-1660)
Thomas Harriot (1560-1621)was another mathematician who lived the longer part of his life in the sixteenth century but whose outstanding publication appeared in the seventeenth century. He is of special interest to Americans, because in 1585 he was sent by Sir Walter Raleigh as a wurvevor with Sir Richard Grenville's expedition to the New World to map what was then called Virginia but is now North Carolina. As a mathemtician, Harrito is usually considered the founder of the English school of algebrists.
His great work in
this field, the Artis analyticae praxis, was not published until ten
years after his death and deals Jargely with the theory of equations. This work did much
toward setting the present standards for a textbook on the subject. It includes a
treatment of equations of the first, second, third, and fourth degrees; thd forma
tion of equations having given roots; the rdlations between the roots and the
coefficients of an equation; the familiar transformaitons of an equation into
another having roots bearing some specific relation to the roots of the original
equation; and the numerical solution of equations. Much of this material is
found, of course, is the works of Viete, but Harriot's is a mare complete and
better systematized treatment. Harriot followed Viete's plan of using vowels
for unknowns and consonants for constants, bur he adopted the lower-case
rather than the upper-case letters. He improved on Viete's notaion for powers
by representing a by aa, a by aaa, and so forth. He was also the first to use
the signs > and < for "is greater than" and "is less than," reapectively, but
these symbols were not immediantely accepted by other writers.
Oughtred seems to have ignored the usual rules of good health and proba
bly continued to ignore them throughout his long life. When he finally died, it is
said that he did so in a transport of joy at receiving the news of the restoration
of Charles II. To this, Augustus De Morgan once remarked, "It should be
added, by way of excuse, that he was eighty-six years old."
ing over 150 of them. Of these, only three have come down to present times:
the cross (¡¿)for multiplication, the four dots (::) used in a proportion, and our
frequently used syboly for
differnce between (¡).
The cross as a symbol for
multiplication, however, was not readily adopted because, as Leibniz objedted,
it too closely resembles ¥ö.
Although Harriot on occasion used the dot (¡¤) for
multiplication, this symbol was not prominently used until Leibniz adopted it.
Likbniz also used the cap symbol (¡û) for multiplication, a symbol that is used
today to indicate intersection in the theory of sets. The Angly-American sym
bol for division (¡À) is also of seventeenth-century origin, having first appeared
in print in 1659 in an algebra by the Swiss Johann Hiinrich Rahn (1622-1676).
The symbol became known in England some years later when this work was
translated. This symbol for division has long been used in continental Europe to
indicate subtraction. Our familiar signs in geometry¡ª(¡) for similar and ( )
for congruent¡ªare due to Liibniz.