180 THEOR. CIRCA DiriSORES NFMEK, cet. 



birmimus , vt in fiirma aa-\-Khb niimeri a et ^ Hnt in- 

 icr le niimeri primi : nifi eniin hacc eonditio obfcruetiir , 

 quilibct numcrui poflct cflc diuifor iftius ftrmne Cctc- 

 rum h;ic conditionc obleruata ex pr.icccdcntAnb pcrfpicuum 

 eft , fi 4Nw« — A(OT-f-«) qu:idnuum cflTc ncqueat, tum 

 quoquc hanc latius pattntcm 4 N ;/? « - A ( w 4- « ) -t- 4 N p 

 (;«-}-«) quadratum cflc non poflc. 



Scholion ^. 



Contcmplemur iam cxprcirioncjn aa — Nbb cuius nullus 

 diuilbr contincatur in finniula hac 4N;;/-4-A. Krit crgo 

 aa — K/fO^^^^i-KmiiA-Au fcu «j^ce^N w«-f-N A A 4- 

 A u. Ponatur N A -j- u — d , (cu m — -4- </ 4- N A , 

 eritquc a aac 4- 4 N ;;; ^ 4^ 4 N N A ;;/ -i- A ^ , fit d zz: 

 4;2 4NN« fictquc i6N*wn 4^ 4NN Aw/ f- 4NN A;; 

 -^aa^ \ndc . patet niiUum numcrum contcntum in hac 

 formula 4N;//;; 4- A(;;/ — ;/ ) qu:idratum cflc poflc. Nc- 

 quc crgo ctiam vUus numcms in hac cxprcllionc 4N;;/ 

 «+ A (;;/ — «) 4^ 4 Np (/;/ — ;;) coutcntus qu:idr;uum cflTe 

 potcrit , fi modo couditio aiuc mcmorata ohllnictur , vt 

 a cz If fiut numcri intcr (c primi. Hiuc itique cx thco- 

 rcmatis poflcrionb.b dcduciiiuur (cquctucs formulac, quac 

 nunquam numcrob quadratos pracbcrc poflliut. 



8w;/4- 3 (;;/-«), 8;;/;;-}- 5 (;;/ — ;/) 



iztn>i-\- 5 (;;/ — «); 12;;/«-!-^ 7 (;;/—«) 



zomn-+- 3 (;;/ — ;;); •zomn-j-iy [m — n) 



2omn-\- 7 (;;/ — ;;); 2o;;/«4-i3 (;« — ;/) 



24;»;;^- 7 (;;/ — ;;); 24;;/;;!- 17 (/;/ — «) 

 24;;/;/4_ii (;;/-;/); 24;««4l '3 ('« — ") 



28;;/ 



