106 



LETTERS ON SCIENTIFIC SUBJECTS. 



equations by ayd of logmes, or by his little table of continuall 

 proportionalls for interest, whereby he finds two rootes at a 

 time, and depresseth the equation two degrees. Whereas 

 Deschartes cubick equation only serveth to breake a biqua- 

 dratick equation into two quadratick ones, \vhereof the rootes 

 are afterwards to be found, and a paire of rootes being by 

 Collins method alwaies found, or two impossible ones re- 

 mooved (by ayd of the rootes of pure powers and adfected 

 equations) one degree lower than that proposed, it follows 

 that solid problems are effected by plaine geometry, et pro- 

 blema Deliacum tandem feliciter expugnatum. Deo gloria ! 



JOHN COLLINS TO MR. OLDENBURGH. 



[MS. Birch, Brit. Mus. 4432, fol. 25.] 



May 25, 1675. 



Sir, Be pleased to intreate the learned and worthy Mr. 

 Tschirnhaus, to make a construction by a circle for finding a 

 roote of either of these equations, which have the conditions 

 he requires 



a a a 3 a a + 3 a 1=N 



In which if a roote be 



Or to this equation 

 a# 

 In which if a roote be 



N is 



N is 





 1 



8 



27 

 64 



8 



27 



64 



125 



216 



Which are the cubes 



of numbers less than 



the roote by unit. 



Which are the cubes 

 of numbers greater 

 than the roote by unit. 



And when he hathe demonstrated the same and illustrated 

 the worke by examples in numbers he hath solved the Del- 

 phick probleme with great renowne, and intreate him to make 

 the same publick in the Transactions, the consequence of it 

 will be that he hathe taken away the two first or highest 

 tearmes in these equations, which renders it probable that 

 the like may be done in other and higher equations, and 

 consequently the difficulty that hath hitherto been crux in- 

 genii will be removed ; this is the thing most wanting in ma- 

 thematicks, and if he doth this, 'tis that I so much aspire after, 



