. Scholion i. 



§. 9. Quo haec exemplo clariora reddnntur, confide- 

 remus numerum primum 13, pro quo refidua reperiuntur; i, 

 4? 9? 3i i-^ 10 1 non-refidua vero: 2, 5, 6, 7, s, ii^ at- 

 que vt forma xx-{-fijy diuifibilis elfe queat per 13, nume- 

 rus n in aliqua fex fequentium formularum contentus elfe debet: 



13X — I, 13X — 4, 13X — 3, 13X — 12, 13X — 10, 



flcque valores idonei pro ifto numero n ordine naturali dis» 

 pofiti erunt fequentes; 



ij 3? 4? 9-> 10, 12, 14, id, 17, 22, 23, 25, 27, 2p, 30, 35, 35, 

 3 8, 40-> 42» 43, 48, 49, 51^ 53, 55, 5<J, <5i, 62, 54, 6tf, 

 68,69,74,75,77,79, 81, 82, 87, 88,90,92,94, 95, 100; 

 quorum numerus vsque ad 100 eft 46. Reliqui ergo n.u- 

 meri qui diuiforem 13 a formula x x -\- njy penitus exclu- 

 dunt, deletis iis qui ipfi per 13 funt diuifibiles, ordine erunt 

 illi; 



2? 5, <^, 7, 8, it, 15, 18, 19, 20, 21, 24, 28, 3 1,32, 33, 34, 37, 4i> 

 44,45,46,47, 50,54, 57,58,59,60,63,67,70,71,72,73, 

 76, 80, 83, 84, 85, 86, 89, 93, 9^^ 97, 98, 99-> 

 quorum mimerus eft 47, ideoque tantum non aequalis priori. 

 Ratio autem, cur multipla ipfius 13 exclufimus, eft, quod de 

 formula .v ^ -h 13 v' v r, vtrum diuiforem 13 accipiat, quaeftio 

 efle non poteft, quia manifefto numerus deberet efie diuifibi- 

 lis per 13. 



Scholion 2. - 



§. 10. Quoniam vis noftrae dcmonftiMtionis clarius 

 in exemplis perfpicitur, contemplemur alium numerum primum 

 19, pro quo nouem refidua funt: 1,4, 9, 16,6, 17, 11, 7,5, 

 Bouem vero non-refidua; 2, 3, 8, lo, 12, 13, 14, 15, 18. 



Hinc 



