Philosophiae naturalis principia mathematica . bens <^irtOuotiente, fuppono b-^p = y, & iilum pro^ fubfliituo, utvides;undenova/t^-^-S.^/S &, rejeftis terminis^^-t-^^^—i^^quinihilo funt asquaies, propterea quod ^fupponiturRadixhujus-y^-^^jy-l-i4=o. , Dei^de termini ^b^-f-^a^^-^ abx dant — j^^^quotientiappon^nidum, & —j~y,-*-^ fubflituendum pro^, &c. y-^aay-^axy — xa^ — x^ = o. Sit f^ = 3^^-+-<z^ j y = b—^-^-^ X, * 4,-to ,.rt3x-3 0 •^ c cS cS ^ b -H/ z=zy j -t- Z» -+- j*^^/» -1- 3^^= -+- ^5 -1- axy -+- abx -H ^A^ -H- aay -1- ^^^ -+- aap X — x ? ; 1^3 -^^&C. -^
Philosophiae naturalis principia mathematica . bens <^irtOuotiente, fuppono b-^p = y, & iilum pro^ fubfliituo, utvides;undenova/t^-^-S.^/S &, rejeftis terminis^^-t-^^^—i^^quinihilo funt asquaies, propterea quod ^fupponiturRadixhujus-y^-^^jy-l-i4=o. , Dei^de termini ^b^-f-^a^^-^ abx dant — j^^^quotientiappon^nidum, & —j~y,-*-^ fubflituendum pro^, &c. y-^aay-^axy — xa^ — x^ = o. Sit f^ = 3^^-+-<z^ j y = b—^-^-^ X, * 4,-to ,.rt3x-3 0 •^ c cS cS ^ b -H/ z=zy j -t- Z» -+- j*^^/» -1- 3^^= -+- ^5 -1- axy -+- abx -H ^A^ -H- aay -1- ^^^ -+- aap X — x ? ; 1^3 -^^&C. -^ibp^ -^-T Tf &c. -1- axp — ,. -^ axq . ^ -t- ccp — <z^x -t- f i-f — x^ — a; -(- abx -1- abx c^ -+- ax ;)-: -4- X -+- r^ (:r -^ - -^ t &c. Completoopere, fumonumerum aliqiiempro^, dchzncy-i-ay —xa = o, ficut de numerali sequatione olfenfum fupra refolvo; & ra--dicem ejus pro b fubftituo. 2, Si didus valor fit nihil, hoc eft fi in aequatione refolvehda nuj- B 3 tus ?.i4 DE ANALYSI. as lus fit terminus nifi qui per x vel ^fitmultiplicatus, utinhacj»»—axyH-Ar=:o; tum terminos ( — «A^r-i-x-) feligo in quibus .v feorfim & yetiam leorfim fifieri potelt, alias per a* mulciplicata, fit minimarumdimenfionum. Et illi dant -^-jpro primo termino quotientis, &l*•H-/ pro y fubrtituendum. In hac y^ — a^y-^axy-—x^-Oj licebit pri-mum terminum quotientis vel ex — a^-y — x\ vel exjv—a^y elicere. 3 ,Sivaloriftefitim?.gin;irius, utinhacy-+-)- —ajy-4-5 —jcy_zv-\-x--^x~o, augeo vel imminuo quantitateraxdonec diftus valore-vadit realis. Sic in annexo fchemate, cum AC (j>^} nullaelUtum CD {y) eil imaginaria, Sin minuatur AC per datam AB, ut BCfiat Af ^tum polito quod BC (^) fit nulla, CD (y) erit va-lore quadruplici (CE, CF, CG, vel CH) realis;quarum radicum (CE, CF, CG, vel CH) quaelibetpotelt elleprimus terminusquotientis,prout fuper-licies BEDG, BFDC, BGDC, vel BHDC delide-ratur. In aliis etiam cafibus, fiquandohaefitas, tehocmodoextricabis. De
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