AD ANALYS. DIOPH. PERTINENTIS. 4t 



primo cafii faciamiis tt-^uurzzcc, quod fit fu» 

 mendo t 'izz a et u :zz b y atque hoc cafu necefle eft, 

 Vt fiat 



{^b — 2 a)( ^b - :i a)zza 



Pro 11'^^ Cafu faciamus 1 1 -{- u uz: 2 c c ^ quod 

 £t fumendo t zz a — b et uzn a ^b y atque nunc 

 neceffe eft -vt fit ( c + 3 ^ ) ( ^r + 7 ^ ) — °- 



Pro Iir'''* Cafti faciamus tt-\-uuzr: scc ^ quod 

 fit fumendo tzz^a-^-^bctwzz^a^b^ tum enim 

 t)b 4Z< — 2/ = 4^ — S^et 4« — 3^=5^ — io^# 

 formuJa ad quadratum reducenda erit {6 a— % b) 

 (a— 2 b)zzD^ hoccft (4^—2 tf)(4^ — 3 «)— P, 

 quae cum Cafu 1""" perfe(Se congruit, 



Pro Caiu denique IV^'', faciamus n + ««:=io«^^> 

 quod fit fumendo t m :^ a ^ b et uzz: a — ^ h f 

 tum enim ob 4?^— 2/=-— 14^ — 2^) et 4«- 3^ 

 =:— 5fl— 15^, formula ad quadratum reducenda 

 crit (3^-4-fl!)(7^+«):=iD, prorfus vti in cafu 

 fetundo. Verum hic notandum eft , cafum tertium 

 et quartum adhuc alio modo expediri pofle, Si 

 cnim pro tertio ponamus tzza-^-^b et uzzb^za ^ 

 ob 4« — 2/z:— 10. fl! et 4^^— 3^r— 2^ — ii^fl 

 formula ad quadratum reducenda erit 2c?(iitf-42^)zD. 



Pro Cafu quarto autem, fi ponamus tz^ci+h 

 ct uzzz^^b-ay ob ^u — 2tzziob— lOa et 4«— 3^ 

 zzz^b— 13. flf, formula ad quadratum reducend? cft 

 (fl-^)(i3^ — 9^):ziD. Verum plerumque quo: 

 ties his duobus cafibus fatisfieri poteft toties numeri 

 Tom.XV.Nou.Comm, F t et 



