114 DE m^MERIS AMICABJL. ATOJ'E ALJIS 



pleint : t )t h.ibcbiiiKiir niimcroriim nmicabilium p;iri;i ; 

 ita ex. §r. iii diiobib niimcris +5 11 ct^. 71 cft \trin- 

 qiic liimm:! diniloriim cadcm \iJclicct 7.6. i2~7. 72-, 

 dcindc h:icc riimm.i diui(i)rimi , in ^troquc cadcm , 7. <J. 12 , 

 aeqailis e;l rumm-.ic numcrorum ; cll cnim 7. 6. 12 n; 



4(55-1-71 ) = 4- i-<^- 



§.20. Pro crnendi et demoii(lr;ind:i mctliodo Carte- 

 Jii prod-icendi numcros :imicabilcs , (iipcrius in mcdium al- 

 lata , pou.imus eire eos AP et AQ; rcquuitur crgo per 

 conditioncm I. vt fit a{V-{- i) — a{(^-\-i) ^ hoc cft 

 P~Q_; qu:uc duo numcri qu;iefiti e^Tciit acqualcs , ct 

 iidcm , qnod cll contra hypothcfui ; ncquc adco h.ic ra- 

 tionc talcs uumcri polfunt indagari. Ponamus ergo cos 

 cflc AP ct AQR. ; rcquiit conditio I, vt (it P-i-izz: 

 (Q__l_i)(R_l_i), vndc Prr(^R-f-q-4-R. Podulat 

 conditio II, vt (it <?(P-hi ) — A(P-h(^R ) ; cx quo 

 fit P zr —r^" 7 ^^ '^^^ valorcs ipfius P , acquati intcr (e , 

 rcddunt (^K -f-Q.+ R — ''V-l'' > ^ R"" dcducitur R — 

 (,J-Via-;.t.' A-T \ qii-^ilis valor ipfius R , primi , vt eo fa- 

 cilith rcpcriatur , ponatur 2A— <7~i, quae proprictas 

 biiwrio compctit i (§ 15.) crit iraquc A— 2"" ; 2Azr 

 jm-f-i ^ ^ — !"'->-' — I j atque ob i\—azn\ , erit<7 — 

 Azz:A — 1~2'" — ij ct valor ipfius R abibit in hiinc 

 altcrum ^ ^_(jj -^ \ vcl , diuifionc aiflu inllituta ^ K~ a 



— A -i- - ^,^I ^vT •> ^ (iibltitutis v;iloribus iplbrum A,rt, 

 modo inucntis , dcducituv Liudem R zr 2'" — i -}- 



Si cx. gr. a(rum:imr otzz:2 , ita vt fit A 



Q_-H I - 2 "'■ 



— ^"•z-^j ciit R— 3-hirii vndc, airumto qiiouis 



pnmo 



