25a DEMONSTRATIO SINGVLARIS 



dem planc cxhibe;int nidicenn. Porro pro noflro 

 quidem cxcmplo , nullum cit dubium , quin feries 

 formae nicdiae rcrpondens fiiu diuergens , \nde ipfi 

 nuHa plane rerpondet radix. Deinde in gericre no- 

 tare iunat , huiusmodi aequationem cubicam 



.v' -h « v' -+- m X -\- t/i n — o 

 fi fnb his rcpraefentetur formis 



.v_i-;/_f. J_l_^ — o et .r-4-«4-l^!^i^— o 

 ad pracfcriptum Thcorematis relolutam , vtroque 

 cafu pracbcre .vir / — — n, nam pro priori habetur 

 Cp; = -:^ -';'?, pro polteriori autem (pi--'llL=± , 

 vtraquc cxprctfionc in o abeuntc, fi pro / fubflituatur 

 — ;;. Pluriniis de cactcro cxcmplis olkndi poteft, pro 

 acquatione cubica. 



A'^~aA'*H-i>.v+t-, fcriem ex forma .v — a-f *-^^~=-^ 

 dcdudam , fiepiu«> ficri diucrgcntem. Tantum igi- 

 tur abcrt , vt per adplicationcm Theorematis Ol. 

 La Grange , omnes aequationum radices alfignari 

 queant, vt planc non conftct, an quouis cafu, prae- 

 tcr vnicam hoc modo dctcrminare liceat ? 



XVII. Si in exprcffione /-.r — (p.v, fundio 

 (J) .V quascunqne quantitatcs tranfcendcntes inuoluat , 

 vaior tamcn ipfius .v aequationi fatisficiens, Theore- 

 mate praefcnti in vfum vocato facile dcfiniri poted, 

 fic fi fucrit / — A-i-«fin..v, quo cafu (p.v=i — ;/fm..v 

 habebitnr 

 \]jx—\bi-n fin t ^' t -\- '^''JiiL-li^Ii - iL^iiyy"-'!^' 



^ ' ' I. t dl I. j. : d /- 



, »!♦ d\,fin . \* >j.' / _ 

 •^ .. 7. ;. ♦ dJJ *-^^' 



Notum 



