— *9 



p 6 



2») fit f — ~ 7 et formula 7 .36-1-3 . 49, "per 7.3 depressa, dat fac- 

 torem 19. Jam 



P 



3°) fit -zzz^, unde formula 7. 14-5.4 dat factorem 19. Tandem 



t— 4 



4°) fiet - — | 3 unde formula 7 . 16 -4- 3 . 49, per 7 depressa, 



-7 



praebet factorem 3/. 



.$. 12. Tertium 'denique exemplum erat 



12091 zzz 7 . 4°" ~H 11 • 9 2 et 



1209 l ~ 7 . 4 2 -+• 11 . 33 2 , ex quo fit 



- zzz "T-fjr^ et formula 7 p p -f- 1199 dabit : 



P ' 

 i°) - — ||; hinc formula 7 . 22 2 -j- 11 . 21 2 , per 7.11 de,- 



pressa, dabit factorem 107. Erit 



2°) ^ zzz ^ , hinc formula 7 . ji 2 H- 11 . 6 2 , per 11 depressa,, 



dat factorem 11 3. Porro fit 

 P 

 3°) -zzz.$, hinc formula 7 . 6 2 -4- 11 . 7*, per 7 depressa, prae- 



bet factorem 11 5. Tandem erit 



4 ) - — | , unde formula 7 . 5 2 -4- 1 1 . 2 2 statim dat factorem 107. 



Theorema III. 



Si fuerit tam N~«aa-4-/3&6 quam N zzz x A 1 4- /3 B ", /unc- 



gue formetur fractio ~zzz ^-fjj-gj tura- ista formula ccpp -\-@qq sem- 

 per continebit factorem numeri propositi N, gui scilicet vel ipse se 

 prodit , vel facta divisione sive per a , sive per /3, siue per «/3, 

 quandoque etiarn per alium numerum simplicissimum 2 , ejusve 

 potestatem. 



Demonstratio. 



- §. i5. Cum sit oi a a +- /3 fr Z? = « A 2 -+ /3 B\ erit «(aa — A 2 ) = 

 /3 (B B - fcfc), hincqoe ^ = |f££»> Sit nunc | fracrio 



