= (53) = 



Hiiic igitur formul.i xx-\-nyY diuirorem 19 rccipcrc pote- 

 rit, fi numerus « in fcqucnti forma contineatur: 



n^ripX — (i, 4, 9, i<5, <S, 17, 11, 7, 5); 

 (in autcm ;; contincatur in fcqucnti formula: 



«=zi9X — (2, 3, S, 10, 12, 13, i + , 15, 18), 

 tum nullus numcrus formae xx-hnjj per 19 diiiidi potcrif. 

 Vulores igitur idouci pro uumcro n vsque ad ceutum ordiuc 

 crunt 

 2, 3, 8, 10, 12, 13, 14, 15, 18, 21, 22, 27, 29, 31, 32, 33, 34, 

 37, 40, 41, 46, 48, 50, 51, 52, 53, 5<^, 59, ^o, <55, 67^ ^9-, 

 70,71,72,75,78,791 84, 8^, S8,89, 90, 91, 94, 97. 98, 

 quorum multitudo ell 47. Rcliqui vcro numeri ad hunc fco- 

 piim incpti, cxclufib muitiplis fpfius 19, crunt uumcro 48 fc- 

 quentcs : 



1,4, 5, <!>, 7^P^ i^ ^^•> I7i 20^ 23, 24,25, 2(5, 28,30, 35, 3<^, 

 39-. +-1 +3, 4+, 45, 47^49, 54^55,58,61,62,63,64,66,68, 

 73, 745 77? 80, 81, 82, 83, 85, 87, 92, 93, 9^5 99) i-o. 



Scholion 5. 



§. ir. Quo autcm facilius intelligatur, quomodo quo- 

 Tis cafu, vbi numcrns n idoncum habcr valorem , formula 

 xx-\-njy diuifibilis reddatur per numerum primum P, no- 

 tetur, hoc fempcr fieri poffe, dum pro jr et ^ numeri non 

 maiores quain ; (P — i) accipiantur, arque adco alterum ho- 

 rum numerorum j pro lubitu accipi polfc. Sir igltur /ri, it;i 

 vt habcatur huec f(»rmula : .r.v-|-«, numcrique « refiduum 

 nafcatur r; tum igitur pro .v .v id quacratur quadratum, cui 

 conueniat rcfidiium P — r, ac manifello fumma .v .v -f- « pcr 

 P crit diuifibiiis. Hoc antcm fcmpcr ficri pofic ciiidcns cll, 

 cum fit « — XP — flj vuuc fit rcfiduum r^P — Uy idcoque 

 ' G 3 i' — ^- 



