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XXX. Hints relating to the Ufe which may be made of the Ta- 
bles of natural and logarithmic Sines , Tangents , &c. in the 
numerical Reflation of adfedled Equations. By William 
Wales, F. R. S. and Mafer of the Royal Mathematical School 
in Chrift’s Hofpital* 
Read June 14, 1781 
T HE firft intimation that I can meet with relating to the 
ufe which may be made of the tables of fines, tangents, 
and fecants, in refolving adfedted equations, is in the latter part 
of the fecond volume of ProfefTor saunderson’s Elements of 
Algebra, printed in 1741, after his deceafe. The profeflbr 
there ihews how to refolve thofe two cafes which make the 
firft and fecond of the following examples, by means of the 
tables ; but it appears, from many circumftances, he was not 
aware that the third cafe could be refolved in the fame manner* 
All the three forms were, however, Vefolved by the late Mr* 
Anthony thacker, a very ingenious man, who died in the 
beginning of the year 1744, by the help of a fet of tables, of 
his own invention ; different from, but in fome meafure ana- 
logous to, the tables of fines and tangents. Thefe tables were 
finiftied and publiftied, together with feveral papers concerning 
them, after his death, by a Mr. brown of Cleobury. In thefe 
papers, befide explaining fully the ufe of the tables in refolving 
cubic equations, Mr. thacker fhew T s that his method compre- 
hends the refolution of all biquadratic equations, if they be 
2 firft 
