js6 DE DiriSORlBVS 



fcm , qiii ex permiiwtione notnnim in qindratum ablro 

 qiicat •, aliter enim pcr candcm hanc opcrationcm iplim 

 niciderc in quadratiim po(rumus. Velutn fi afllimamus 

 numenim 1677, qui nulla notarum tranrpofitionc quaUra- 

 tus fit , is fubtrad:o 2 fii 1675 non diuifibilis pcr 3 y 

 f\ igitur ad hoc obtinendum mutarcm 5 in 4 > ^"^ 7 in <5 , 

 emcrgereiK mimcri KS74. ct 166$ , diuiubiles per 3 , 

 fcd vterquc pcr tranlpolitiouem notarum quadratus , fcili- 

 GCt 1764. ,^ et 6s6i. Problcma igitur de lok) tali mi- 

 Bicro intclligendnm eft , qui pcr tranrpontioncm notarum 

 fituum quadratus ficri poflct ; hoc eit , qui abiejflis nouc- 

 nariis relini]tiit vel o , i , 4. , 7. Secimdi) propofiti i\- 

 lis mimeri dcbent mucaii ntxac diiae j vna (ubtraLlo 2 , 

 et hacc extima quidem ad dextram ; altcra autcm intcr- 

 media , vt rcGduum hoc fcit diuifibilc per 3- Nam fi 

 afliimercm exempli gratia numcrum 14.S9 , qui quadratus eft 

 his ipfis noiis ita fcriptis i 849 , at.]ue ab illo fubtrahcrcin 

 2 , vt fiat 14-87 , ct tum notim vltimam mutarcm in- 

 5 , vt ociiUur multiplum 3 , obtincrem fic 14-85 , qui 

 quadratus fit notis in 5184. traafpofitis. 



§. 12, Sed dolcndum cfl , p:iTum airxilii (rahi poflJi- 

 cx praeceiientibus formulis ad indagandum iwimcri alicuius 

 dati diiiiforcm. Liccat igitur tcntarc ali:im adhuc vi;im ,, 

 quac aliquanto phis fublkiii nobls fubmiuiltrabit. Qtiim- 

 uis deflituatur Arirhmctica tali formula gciicrali vnica , 

 qihie nmncros primos omncs (ucccflTuic cxhib&u : certum 

 tamen eft , omncs illos ccxitincri his duabus , nvmpe 

 omnis numcrus primus eft vcl <S;«H-i , vcl <?w-j-5,, 

 Omuis enim numcrus , pcr 6 duiifus , rclinquit vcl 

 0,1, 2, 3, 4., 5, adcoqiic omnci« nuuicri in gcneiG 



coati- 



