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XXX. Hints relating to the Ufe which may he made of the ^Ta- 
bles of natural and logarithmic Sines , Tangents, See. in the 
numerical Resolution of adfeSled Equations. By William 
Wales, F. R . S. and Mafer of the Royal Mathematical School 
in Chriff’s Hofpital. 
Read June 14, 1781. 
rriHE firft intimation that I can meet with relating to the 
A ufe which may be made of the tables of lines, tangents, 
and fecants, in refolving adfedled equations, is in the latter part 
of the fecond volume of Profelfor saunder-son’s Elements of 
Algebra, printed in 1741, after his deceafe. The profelfor 
there fhews how to refolve thofe two cafes which make the 
firli: 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, refolved by the late Mr. 
Anthony thacker, a very ingenious man, who died in the 
beginning of the year 1 744, 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 
finifhed and publilhed, together with feveral papers concerning 
them, after his death, by a Mr. brown of Cleobury. In thefe 
papers, belide explaining fully the ufe of the tables in refolving 
cubic equations, Mr. thacker fhews that his method compre- 
hends the refolution of all biquadratic equations, if they be 
2 frft 
