Hypothells III. 



Qua omncs Tcrrae regiones vera quantitate in plano 



rcpraeientatur. 



§. 5S. Conftitutis in gcncrc binis formulis pro dx 

 et dy , quac fint 



d x~p du-\- qdt ct dy~rdu-\-sdt 



primum efficiatur , vt omncs meridiani a parallelis normali- 



ter traiiciantur , id quod cuenit fi fuerit — — — £-. Statuatur 



i i r 



igitur s~ — n p et q~\- n r vt habeamus 



dx~pdu-\-nrdt ct d y ~ r d u — n p d t. 



Nunc igitur crit clementum PQ — du~V pp-\-rr et elemen- 

 tum Parallcli PR — ndt V pp-\-rr. Hinc igitur area reftan- 

 guliPQRS erit ndudt{pp-\-rr) ; in Sphaera autcm area 

 refpondensp^ri - eft zzzdudt cof. u , quae ergo formulae ae- 

 quales funt reddcndae, \nde fit n{pp-\-rr) ~cof. u ideoque 

 n — _-g^L_, quamobrcm pro noftra Hypothcfi habcbimus has 

 formulas: 



dx—pdu-^ni^-JL ct dy~rdu-* d, " r ^-. 



1 pp-hrr J PP~+- r r 



Quacri ergo oportet funftiones idoncas pro p et r , vt ambae 

 iltac formulae fiant integrabiles. 



§•53- Quo hoc facilius effici poflit flatuamus 

 p~m cof. <$> et r ~ m fin. (|) 

 vt fit pp 4- r r — m m ct habcbimus 



d x~m du cof. (p + ii^L^JHhl et 



tfl 



d y —mdu fin. t£> — d ^ r - "»/•$ . 

 Fiat porro wrr&cof.tt \t confequamur 



d x—kducoC.u cof. (£> -f- ^iJi^ e t 



dy~kdu cof. tt fin. - £!f£±. 

 Jcia Acad. Imp. Sc. Tom. I. P. /. R Facia- 



