Methodus inveniendi lineas curvas

70 DE METHODO MAX. ET MIN. H | $y, p, q, r, s, t,$ --|------------------------------------ I | $y', p', q', r', s', t',$ K | $y'', p'', q'', r'', s'', t'',$ L | $y''', p''', q''', r''', s''', t''',$ M | $y'''', p'''', q'''', r'''', s'''', t'''',$ N | $y''''', p''''', q''''', r''''', s''''', t''''',$ Hi autem finguli valores a tranflatione n in $\nu$ fequentia augmenta accipient, quæ ex Propofitione prima, debita mutatione fignorum adhibita, ita fe habebunt. $dy=0$ | $dy'=0$ | $dy''=0$ | $dy'''=0$ | $dy''''=0$ | $dy'''''=+\frac{n\nu}{dx}$ --|---|---|---|---|--- $dp=0$ | $dp'=0$ | $dp''=0$ | $dp'''=0$ | $dp''''=+\frac{n\nu}{dx}$ | $dp'''''=-\frac{n\nu}{dx^2}$ $dq=0$ | $dq'=0$ | $dq''=0$ | $dq'''=+\frac{n\nu}{dx^2}$ | $dq''''=-\frac{2n\nu}{dx^3}$ | $dq'''''=+\frac{n\nu}{dx^3}$ $dr=0$ | $dr'=0$ | $dr''=+\frac{n\nu}{dx^3}$ | $dr'''=-\frac{3n\nu}{dx^4}$ | $dr''''=+\frac{3n\nu}{dx^4}$ | $dr'''''=-\frac{n\nu}{dx^4}$ $ds=0$ | $ds'=+\frac{n\nu}{dx^4}$ | $ds''=-\frac{4n\nu}{dx^5}$ | $ds'''=+\frac{6n\nu}{dx^5}$ | $ds''''=-\frac{4n\nu}{dx^5}$ | $ds'''''=+\frac{n\nu}{dx^5}$ $dt=+\frac{n\nu}{dx^5}$ | $dt'=-\frac{5n\nu}{dx^6}$ | $dt''=+\frac{10n\nu}{dx^6}$ | $dt'''=-\frac{10n\nu}{dx^6}$ | $dt''''=+\frac{5n\nu}{dx^6}$ | $dt'''''=-\frac{n\nu}{dx^6}$ Quoniam porro valor formulæ $\int Zdx$ abfcissæ AH respondet, isque a tranflatione puncti n in $\nu$ non mutatur, fequentibus abfcissæ elementis valores formulæ $\int Zdx$ respondent, qui in hac Tabula exhibentur. Elemento | respondet --|--- HI | $Zdx$ IK | $Z'dx$ KL | $Z''dx$ LM | $Z'''dx$ MN | $Z''''dx$ NO | $Z'''''dx$ Adhuc