AD ANALYS. DIOPH. PERTINENTIS. 39 



nique eezrgg, vbi fumi poteft fl!=iH-fi( et ezzA-g, 

 Tum vcro quatuor noui valores pro z inueniuutur 

 fequentes ; 



I. S ~ /■ 4- -'a(f>e ^ad) 



ae^ -i-d d — cf g 



II. zzzf^ _, 



JU^ ^ — /-4- Cz^^^H-gcrc — Z>&)f;a»f — aa e^hh) 

 ' ■^ 4aQ(2C'd — aahc-^b*) 



ly ^ — f— 1— ^ e e{ Th e — cdee -^d^ ) 



-^ ' ^2a e^ -i~cee — ddji ^a e'^ —-cee-i-dd) 



quoniam igitur quemcunque valorem pro z hoc 

 niodo inuentiim afTumere licet , hinc numerus foJu- 

 tiouum m infinitum augeri poterit. 



17. Poftquam autem pro z valor quicunque 

 jdoneus fuerit inuentus, qui fit ^f^ij^, ob szi^z:^—^, 

 tiabebimus mzzb et nzzzb—ky ex quibus dnobus 

 Tiameris 7n et n reliquae quantitates fequenti fi.odo 

 determinantur : 



pTziimm—imn-\-nn\ qrzmm-\-mn—nn 

 szzmm-\-mn^nn '^ rzzmm "imnzzmim-^nn] ^ 

 vbi notafle iuuabit effe : 



pp^ss::z[mm-\-nn){smm — 6mn-\-!inn) et 

 qq-^-rrzz^mm + nn^^iimm— ^mn-^-nn^-zi^mm-^-nn^p^ 

 fltque hinc dcnique ambo noftri numeri quaefiti erunt 



A ( m r\ -f. n ■n)'^ { STn -m — emn -f- ^nn) ^^ 



4 771 ( m - 2 n ) ( rn m -t- m n — n n)- 

 T> {m.m -^ n ny- [ 5 vi vi — 6 m n ->- 2 n 7i ) ( ; 77t tti - 2 tn w 4- n n) 



"■ (3 TTl 71 )■* ( 771 71 )' 771 n ( 771 — - 2 T; J ( 2 771 -}- 7;} 



18. Vt autem etiam innotefcat, quemadmodum 

 Jiuiusmodi valores iuuenti ratisfaciaut, exbiuisxiumeris 



idoneis 



