S% SOLVTIO PROBLEMATIS BlFFlCILLmT 



y akcmntiu-. \'criiin valor ipfuis z variationcm fubit 

 ex quo pro z fcnipcr diiplcx valor alVigiv.ui potcrit , aU 

 ter qui iam cft cxhibitus z — x-\--^-^Tr~ ^lf^r vcro ;2 — 

 ^v-f--^^^''- : ficqiic ob dupliccm valor<;m ipfuis z fia- 

 gula cxcmpla allati duplicnbuntur. 



§. i8. Huiii-modi folutioncs particularcs pliircs ad- 

 huc cliccre licct , diim aliac idoncac quantitatcs pro radicc 

 quadiata himis formac ^p* -+• ^q* — ^qqrr-\-r* a(la- 

 muurir. Vchiti fi hacc radix ponatur rr -\- zqq-j-2. 

 'pp, obtincbitur hacc acquatio —-^qqrrzm^qqrr-^Ji^pp 

 {zqq -{- rr), fcu pp{iqq -\- rr) ^ -\- zqqrr\, vnde 

 patet fignum infcrius valcrc , cflcquc V(4.v.v-t-j;>') — 



rr-\- zqq-zpp, cxiacntc vcl p—:^jT~;:p; vel^r 77^^,-^) 

 •quac formuhic iam ficile rat.onalcs rcdduutur. Uic {:xdp 

 fi ponatur ri^ 3 , />— i, crit q — l, ct in intcgris 

 ;p — 4. .V ~ 16 qui cafus ob y ncgatiuum 

 ^—3 y——iz6 non conucnit quacstioni 

 .r = I c V ( 4 .V X -{-jy ) rr 1 3 o 



§. 19. Qmiam cardo qu.icflionis in hoc ver(-itur,, 



'Vt hacc cxprcifio rcddatur quadratum, 4-/)*4-( 2</</-rr)\ 



'potcll hoc gcncralitcr ita cffici, vt cius radix ponaiur zr 



£^^_r/--f- •"/>/>, vndc fict ppzz."^ [i qq-rr^-^-^^^pp 



fcu {un-mm)pp = wn[2qq-rr), ct /.-V^V.'^ 



■'•zz uni V ~l^^^^^ ^ cui conditioni (atisfiet ciusmodi ni^ 



rncros pro m ct n quacrcndo , vt fit mii[nn — mm) nu- 



'mcrib huius ff)rmac "^JJ—gg. Vcnim hacc (okitio facili» 



141S obtinctur ex ipf» praeparationc ad (i)lutioncm tradita , 



*fju.ic , fi rC(5lc tratlvtur , omncs lokitioncb iion (blum 



■ m- 



