Johannes (I) Bernoulli. 



Ex. gr. Vax+xx differentialis est 



a dx + 2x dx 3/ .... , a dx + 2x dx 



vax+xx différent. 



2 Vax + xx " 3D^ 



ax + xx 



-3/ 



V d X + X X 



Ad inveniendam differentialem quantitatis =. Inventa 



Vyx+yy 



differentiali — — = Numeratoris, ut et differentiali Deno- 



SL2Vax + xx 



. r „-, y dx + x dy + 2y dy _ . K T 



mmatons [7J = — per Kegulam 5. Invemtur 



2 vy x + y y 



per Regulam 4: 



adx + 2xdx ' . ■ , — -ydx~xdy-2ydy. 3/ 



= m Vxy + yy + - — ~ — — — in vax + xx 



SOVax+'XX 2 vxy + yy 



xy + yy 



■A / fl rp l_ rp rp j ~~ ~~ ; 



differentialis ipsius — Quantitatis Vax + xx + Vaay + y z 



vyx+yy 



.... ,. .. , 2adx + 4xdx in Vaa y + y z + aa dy + 3ww dy 

 differentialis est = tf * - uu b • 



QVax + xx + Vaay + y 3 in 2 Vaa y + y 3 

 [8] Diese Seite ist leer. 



[9] De Usu Calculi Differentialis in resolvendis 

 Problematibus. 



Problema I. 



Invenire Tangentem Parabolae. 



Est ex natura Parabolae ax = yy. Ergo etiam adx = 2ydy. 

 Igitur a ' 2 y :: dy • dx.*) porro, quia unaquaevis linea Curva ex 

 infinitis lineis rectis constare intelligitur per Postul. 2 erit Tangens 

 AD et portio infinite parva DF parabolae BDF una linea recta: 

 Ducta itaque (Fig. 1) Diametro AE parallela DG, erunt Ala 

 DGF et ACD similia. Quocirca FG • GD :: CD • AC id est 

 dy • dx:: y • s (subtangentem) :: a • 2 y (ex anteced.) igitur s = 



^- = - - — = 2 x. Si itaque A C sumatur dupla ipsius abscissae 



0/ Cl •* 



BC, et per punctum A et datum in Curva punctum D ducatur 

 recta AD, erit illa Tangens. Q. e. i. 



*) In heutiger Schreibweise a : 2 y = dy: dx. 



