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P r h l o m a IT. 

 Invenirc îineam curvam ternis coordinatis x, y ef z con- 

 tentam, in qua haec jormuîa integralis: f ^^ l^'^ 

 maximum ininimunwe ohtincat valorem. 

 S o 1 u t i o. 

 l6. Posito hic dy =^pdx cl. dz=: p^dx z:^ qdx, erit 

 V z^ pq (y -+- 2-) , hincque dilïcr'entiando : 



dV — pqd/^pqdz-h (y + z) q^P +• ( J + z-) /^ 5 7- 

 Unde , fiicta comparalione ciim formula generali : 



habebiimis MnzO; Nizipf/; Wzizpq; P = (/ + z) 7 et 

 P^-(y-h%) p; hinc ergo fict S = V — P/j — P'(/ = — pf/(/-+-z). 

 Ex his jam très nostrae aequationes. crunt : 



1°. ozz-^d.pq .(y^z); 



2°. pqdx-d . (y ^ z) q; 



3°. pqdx =: ^ . (/ -|- z) p. 

 Prima statim praebet pq (y-i-z^z^a, ita nt sit y + zz=z~, 

 qui valor , in reliquis substitutus, dat : 



1°. pqdx=zd.- — — -jf; 2°. pqdx — d.^— — —, 

 Hinc sequitur fore -| =: -; consequenter — ^ :zi — '--+-6,. 

 sive ^=:-H-b, tmde elicimus qzzz.-^-^. Sicque prima 

 aequatio ï\t y -^ z— "^--^' ; reliquae vero dant pqdx — —^, 

 Mecque 3 x = — ^-^— "i^-— > ciijus integi*ile praeDet. 



c p p ^ 1 '' PP 



c p■^ 

 X — -?- J ~ u f 



