Opuscula. 
6i 
Itaque coordinatae T coordinatis x, y plani 
alterius pofitione dati HGS exprimi poterunt, fi fiat 
I. X— qmx-\-qny-{-fz,, 
II. Z :=z qz, — f mx — / • 
Wl.r — my — nx. 
IV. Z^ -f- r 1=: ( -4- ) A-^ -f- ( ) / -4- q"- z,* 
— 2mn{i — p^) X y — i m f qx z, — inp qyz» 
V. XZ — — m^fqx^ — n'-pqy^'-\-fqz,'- 
— imn^qxy-\-m {q^ — p*) xz>-\-n {q^—-f')y^» 
VI. XT — — mnqx^ -\-mn qy"- 
~\- q {m^ — n^)xy — n p x z ~\- m ^ y z, , 
Quod fi elementum totius corporis fit d M , eoque ad pla^ 
num HGS relato innotefcant fummae omnes , ac fiat 
fx^dU-A fxydWl — D 
fy^dU—B fxz>dM=E 
fz^dNl=:C fyzdM:=zF, erit etiam 
VII. fY'~r,dM — {,i'-^m'f) A-i-{m'-\-K'p')B-hfC 
— 1 m n q^ D — ■ i m p q E — i n p q F , 
VIII. fXZ.dM—-^m'pqA — n^pqB-i-pqC 
— imnpq D-\-m {q^ — p^) E-{-n {q^ — p^) F, 
IX. fXT.dM— — >nnqA-i-mnqB 
-\-q{m'- — «^) D — npE-\-mpF. 
Cum dato corpore dentur fummae omnes A^B^C^D^ 
E , F) fi quantitates etiam p , q pro conilantibus accipiantur, 
& (olx m , n fint variabiles , atque elementum variabilis 
anguli SGL fit , ac fiat dn =zm du ^ & d m — — . n du ^ 
ob I — p^ — q^ ^ fiet d { n^ + m^ p^ ) A = imnq^ Adtt ^ & 
d{m^ -\- p^ )B — — 2 m n q^ B d u], eodemque ordine fumptis 
elementis omnibus terminorum , qui lummam omnium 
Z^ -\- T^.dM exprimunt , fiet in pundo quocumque P 
quantitas Z^^^hT T\dM==~iq du .fX T.dM. Pariter fi 
&'« pro conftantibus , p vero , & q pro variabilibus 
accipianrur , & fit dnj elementum anguli variabilis LGT , 
pofito d.p^ — ipqd^y ^d.q"" — — ■ 2 ^ ^ ^ , eodemque 
modo aliis omnibus elementis fumptis , fiet in pundlo eodeni 
P quantitas Z''^ T- . dM == — i d ^ .fX Z . dM . Quare fi 
binos angulos SGL , LGT, eorumque finus , & cofinus fi- 
mul variari intclligamus , erit Z"" -\- T^.dM =z — iqdu 
jXT.dM-^zdnj.fXZ.dU; & fi quo in cafu redangu^ 
