ECONOMY OF LABOUR IN MATHEMATICS »; 



of convergence, and had given numerous graphical illustrations 

 of the j>.it hs. pursued in Approximating to 1 1 1 < ~ rool . ' 



Now, although Dary was well Acquainted with cartesian 

 geometry, he gives no graphical illustration ol his method, 



and there serins to he no reason to suppose h< - had considered 



the possibility thai his method tnighl fail to give a commensui 

 ai)ic pool hi finite terms, oi to give the roots when two oi 

 more roots are nearly equal, or thai ii< - had considered the 

 rate "i convergence of ins luccessive tubstitutions. 



Thai the method ol approximation usually called Newton's 

 method should ratlin he called Dary's method will be icen by 

 those win) are familiar with hi • work •, the chiei oi which are 



i. I hr Genital Doctrint <>/ Equations numerically laid down 

 in three chapters concerning the Invention, Reduction, Solution, 

 of an Equation, Printed foi iii<" author In the yeai 1664, 

 1 ondon. 



■ iKnv'. Miscellanies, London, 1669. 



1,. Interest Epitomised both Simple and Compound, l on 

 don, 1677, 



4. I he Complete Gauge* in Two Parts Theoretical and 

 Practical. By Michael Dary, IMiilomathi London, 1678 



hi the lii " .1 ol these work., h.ny <\>a\ . mOSl fully With M i<- 



lolution oi equations and also with interest problem!*, and 



l^i vrs 111 tabular Ini'in thr solution "I I In- whole twenty equation ■ 



connected with a geometric progression, i.c, 11 I be the ftrsl 

 term, fi th<" last, R the ratio, /v the number oi terms, S the 

 .inn ol ,V terms given any three ol these quantities, find 

 the remaining two. 



Now the point which in this papci we most desire to bring 

 to the notice ol our readei 1 ■, the Kreal numbci oi times this 

 method ol iteration (due to Dary) 1 pops up , 1 egeudre, in the 



Supplement a i I: ■ -m .ur In llieotn diS NombtSS, ICCOnd <'lilnui, 



Fe*vriei 1816, introduces the metliod and considers functions 

 wlm 1 1 he calls " fonctions omales," whii h always me cease "i 



always (In i c;i ,r. 



' Oil J.uiu.iiy I'/, 1909, I incivrd ,i MSS limn \ii I'l.inM I'm., in 

 Which l»C ffilVC .1 p .mil' "I In. v<i/ IXtfllllvl I --..,,, |,,- . ,,,1,, ||,,- Solution "I 



Equations l>y Iteration, considering 1 1 » *— method* ol iloiding wiiii thi ruoldity 

 of convcrycncy oi divergency md the. meMurc oi oBclllmion of the d< ending 



ami ,r.i rii'liii); -.ri i'- . i.l n|ni iii-.n . p willi lUggfltiOfll I"' the Rpptll itlon til ■ 



to iiuiiiciou. wrll known tvjo.il mug. 



