C 94 3 
Sit t=3i s~m— • 3 ; habebitur coefficiens ipfius 
, m.m — i.m — 2 .m — 3 •/»* — 4 1 
? 0j> — 1 1 — — — 
1.2.3.^ " 3 5* ••*•••• x 
m . m — t . m — 2 
1.2.3. 
j & flc de cxteris. 
Si quis forte dubitet, an fuperior demonftratio 
evincat omnes terminos neceflario formari tot modis, 
quibus poflunt, & contendat earn tantum oftendere id 
accidere pofle, hoc refponfi ferat. 
Ccncp -\-q\ * =p -\~qXp -\-q\ j fed inter hujus 
terminos funt p m " r ‘~ x q ,, i & p m — n q”~\ quse neceflario 
ducentur in p & q, & p m ~‘ n ~~ l q tl xp~p m ~ n q n =- 
pm-nqi - ergo prn-n^i omn ib us modis poflibilibus 
fadtum erit in pX°X > p m ~ n — x q n & p m - M q”“ l fmt ge- 
nita quot modis poflunt in p^~q\~ l ; quod neceflario 
erit, fi p m — n ~ z (q n , & p m ~' n q n ~ z fint in inferiori poteftate 
p-\-q\ \ & flc femper ufquc ad quadratum in quo 
pp,pq-> & q q habentur, effi&a tot quot poflunt mo- 
dis (4. II. Euclid .) ergo & in fuperioribus. 
Hoc ratiocinium monet, ut idem etiam fic often- 
dam, ratione paulo diverfa. 
Jam primi coefficientem efle unitatem demonftra- 
vimus. 
Secundus terminus p m ~ x q conficitur ex p m ~ z qxp 9 
& p m ~ x Xq, id eft, ex primp radicis in fecundum ipfius 
— i ,m— 1 I 
p\q I , & ex fecundo radicis in primum^-J-^1 , 
- ■ ■ ii ■ jyi 
ergo in p-\-q\ adeft p m ~ x q feme), plus toties, quoties 
fecundus eft in />+$ | , qui ibi eft femel, plus toties, 
quoties fecundus in p-\~°X ’ qui rurfus ibi eft femel 
plus 
