[ lopp] 
whole procefs of many Operations is at once expored to 
the Ey in a Ihort Synopfis. 
By help of this he makes mainy Difcoveries, in the pro- 
cefs 0\ Algebra, not before taken notice of. 
He introduceth alfo his Numeral Exegejis^ of affeded 
Equations, extracting the Roots of thefe in Numbers. 
Which had before been applied to fingle Equations, fuch^ 
as the extrading the Roots oiSquares, Cuhes^ 6c. fingly 
propofedi butliad not been applied ( or but rarely ) to 
Equations afFed:ed. 
And in the Denomination of Powers, lie follows the or- 
der oiDiophantuH not that derived from the ^r^^/, which 
others had before ufed. 
The method of Fieta is followed, and much improved, 
by Mr. Otightred'm his Clavis ( nrft publiflied in the Year 
1^3 I. ) and other Treatifes of his, -and he doth therein, 
in a brief compendious method, declare in fhort^what had 
before been.the Subjed of large Volums : and doth, in 
few fmall pieces of his, give us the Subftance and marrow 
of all (or mofl of) the Ancient Geometry. 
And for this rea (on, I have here interred a pretty foil 
account of his method, together wiih an laftitation for 
thepradiceof^/^e^ r^ according thereunto. And,though 
-much of it had been before taught in the Authors above 
mentioned, yet this I judged che mofl: proper place to m- 
fertfuch an luilitut on^ becaufe by him delivered in the. 
mofl: compendious form. 
And in purfuance of his mcrhod, and as an Exemplifi- 
cation thereof, I have here added (befide 1^» me Examples 
of his own) a DilcouxiQ ot Angular SeBioru, andleveral 
things thereon depending. Bat this ( thac it might not 
j £eem too great a Digreffion in the body of the Book J I 
have fuhjoined at the end as a Treatife by it ielf ; as, for 
the like Realon, I have done fome other things s to which 
t the principal Treatife doth ( in the proper pkces ) refer. 
Mr. Harriot w^s. contemporary with Mw G.ugl7tred^ 
