SrSir

I have lately tryed to looke into Cartes 3d booke of yethe nature of æquations, thinking to understand what goes before by yethe helpe of his rules delivered there: & I begin to hope I may by my owne strength, & j judge it is better to find one conclusion out than have 20 shewed me, wchwhich made me defer moving questions to you so long, & partly because j cannot move my many doubts in proper termes. But I know you are to good & wise to deride me. Some things Rules I think j understand in ytthat discourse of æquationæquations, but I stick at yethe first hypothesis pag 69th. for first though I may suppose ytthat x is æquall to 2 or x − 2 æquall to nothing &c: –; yet methinks this does not reach yethe yethe universall nature of æquations, though some may be imagined so to be made & then all things follow according to yethe subsequent rules. let x − 2 be 0 yethe & x − 3 = 0 x − 4 = 0 yethe first magnitude ytthat rises is xx − ex + 6 & yethe cube (if j may so call it) x3 − 9xx + 2bx − 29. But set you thus x 2 x 3 x 4 then yethe first æquation on each hand is xx = 6 yethe 2d æquation x3 = 29 Now heare all yethe midle species are lost, such as −9xx + 26x. In yethe next place why must I alter yethe value of x & make it some times æquall to 2 & some times to 3 methinks this is more like a square x − 2 = 0 x − 2 = 0 & xx − 4x + 4 0. &c:

In pag. 74. I cannot understand yethe note H.

pag. 78. I cannot find out yethe order of dividing yethe noted æquation by yy − aa − cc. neither am j able to find yethe meaning of those words in yethe bottome of yethe page. Id quod monstrat radiem quæsitāam esse aa + cc quemadmodūum per multiplicationem probari potest

pag. 79 yethe rule of making 2 æquations + x4*.pxx.qx.r &c. I have practised upon some of his æquations but have not yethe reason of it nor Basins demonstration. p. 137. Nor yethe rule p. 81 of making 2 æquations out of one.

I remember Cartes says if one try methodically to examine his rules, one shall find yethe demonstration of ymthem, be pleased to shew me yethe methodicall examination in ytthat aponation pag. 78 or some other.

pray sir if you can spare time to ease a doubter, deliver a note to Mr Michell or Mr Yard of Kings & they will send it to yoryour

humble & thankfull pupill

T. Horne

Hadly Suffolk. Aug. 22d.