AD ANALYS. DIOPH. PERTINENTIS. 43 



pro altera vero folutione 



t :=za -\- 2 b '^ ??t r^ :i b — a ; 



u— 2 a " b '^ n::z/^b — ^a; 



p—siaa— 2ab-{-2bb) ; rzr— 5(5 — ^)(3^ — a) 



qz:^— S {aa — ab — bb) ; szz:— s[^^ — ^h — bb) 



p a a — 2 a fe— f- ^_^ i> . ^ ct 



— ab-^bi 



s aa — ah — -bb ' r {^a — b){zb — a) 



vnde manifcftum eft has duas folutiones a fe inui- 

 cem non difFcrre. 



23. Speciales nutem folutiones , quae ex hac 

 formula primo intuitu deriuantur funt fequentes 



a 



o 



4 

 12 



quarum binae priores fcopo noftro non conueniunt , 

 tertia vero idoneam praebet folutionem atque adeo 

 ab illa, quam olim iam inueni diuerfam ^ quum enim 

 fit pp-}-xj=z 8957— 53. 1(^9 et ^7-f-mi3922i 

 =^ 53. 74 crunt ambo quaefiti numeri 



A 



B 



16 . sj^.r* 



l6r. 53^ 



4.74.59 .21 4.21.59"' 



I (5p. 7*. >^^ — ■ Igg. ;7. 5$' 



16. 



:. 16. 3. 5-. 7*19- 



5-. 7. 19' 



24. Confiderem.us autem attentlus hanc for- 

 mulam : (4^— 2^)(4^>-3flf):^n et quia numeri a 

 et ^, funt catheti trianguli redanguli , atque eui- 

 dens eft, pro a fumi debere parem pro b vero im- 

 parem, ftatuamus f?zi; 2 ^^ et biizdd—ee^ \t fit hy- 



F 2 pothenufa 



