JD AEQTATIONES LOCALES REVOCAVIS.j,^ 



Inuento pkno tangente fiicile eit liiperficiei in D" 

 perpendicukrem ducere , aHo euim opus nou eft quam' 

 vt in piuido coutadus D plano tangente perpendicu- 

 l^ris ducatiu-. Saepe tamen pracllat per meciiodum di- 

 redam duccre perpendicukires ad ruperlicies , absqiie prae- 

 CippoHta notitia modi ducendi plana tangentia. 



IX. Hic modus diredus duobus \erbis exponi pot- 

 eil. PerpendicuLiris enim ad liiperfkiem eft breuiifi- 

 ma diibntia iuter puniflum horizontis , in quo perpen- 

 dicularis ipii occurrit et iuperficiem propofitam. Hanc 

 ob caufam perpendicularis in quacunque iiiperiicie per 

 methodum de maximis i'eu minimis uiueitigari poteft. 

 Sit ergo P puu(ftum illud in plano liorizontis ex quo 

 breuiilimam lineam ad fuperficiem ducere oportet, ex quo p-;g. ^. 

 perpendicularis PM in dircAriccm VT dcmiiia iit. 

 Deinde ex pun<flo D iiiperficiei ctiam dcmiifi fit DC 

 OTthogonaliter in horizontem , ductisque ex C duabus 

 CB et CN, liic ad VT, iUa vero'ad PM parallchs, 

 dicantur C N =r B M zi: ;« , N P rr ;/ , D C -- :c, et PD^p, 

 iuuenietur pnrV (;«--+-«- -i- c;- ), quae mmima eiie 

 debet. Qi.iare differentiando aequationem p-zi:m--\-n^ 

 -]-z-^ pofita primum m conftanti , fit Jidn-A-zdzzz: 

 pdp—.o^ vel propter 'MP~j'-\-n inuariatam neceifc 

 efl, \t f\t dj --{- dn = , vel dn — -dj^ ~-ndj-\-zdz 

 ~o, adeoque « — ^. Sed aeqnatio fuperficiei z- zr. 

 ax-\-bj^ cum X manens eft , pracbet •zzdz-~bdy ^ 

 adeoque ^^~^b^ quare nzzz-^^b. 



Simihcer diferentiata p- — ?n- -'i- n- --\- Z' pofita ^ 

 eoiifhmti pr aebet m dm -+- z d z— p dp zz o ^ e t quia A M 



F 3, • —A 



