128 OpUSCtJIA . 
braicce; quoniam u.-=z x ^ ^ y=z 2^ apc t & fiimptis differen« 
tiis du=zdpc, dy -^—^-^zr- ^ formula in fequentem tranfmu- 
tabitur 5 iiempe dx V i = - — 7= ; ergo q = -pr , & 
r'-"^ T-» I adx o 
i — qq-z^—^, ErgO U^Jl—qq^ — ^ & 2 = 
1 f 1 .X — 
" - '^' ' ; quantitas curvjs jungenda r=.zq^ erit 
sequalis 2 V . ^ . Coordinatiie. curvse inveniuntur i^a. 
^ X — a i x~ia. Defcripta hac curva ejus arcus , qui ita 
accipiendus efi: , ut crefcat crefcente ^ , vocetur == L fubftitu- 
tis congruis fpeciebus in formula ff^* — L = f ^du'- — dy'*' 
erit 1 ^ X .\Jx—a — L = J d it^ — dy^ . Quire hoc valore 
fubftituto in formuia numeri 15 erit 2 ^ x . y/ x — ^4- 
f — ' — z=z z^x .^x — a — L i five f ..-.JL =: — L , 
five f^-~==.— lj-i quse ofcendit formulam integrari per fo- 
sj X — a, 
lum arcum curvx algebraica: iine ulia additione quantitatis 
algebraiccg . 
§. 17. Determino modo curvam . Primam ordinatam voco 
= rr, , fecundam — 71 . Erit ergo \ a . x — mm^ &;v — ' a 
^ ?2 a ; adeoque ( Fig. a. ) 4^, n -h a =. m m , quja eft 
ad parabolam apollooianam . •Parametro = 4 a defcribatur pa- 
rabola A F C , cujus abfcilTiE r= A E a -f" , in qua fedla 
A I =: , erit I £ = ^2, & ordinatss E F = m . Produc E A in 
D , donec A D =: ? erunt DE — ^^-h 1 a z= ^ ; quare exi- 
ftentibus D E =: ^ erit A F = f^^-^d^ . 
§. 18. RealT-imo pro fecundo exempio formulam loga- 
rithmicam numeri 9, qua^ per Bernouilianum Theorema 
ad integrationem perduci non poteft , quando eft x<^a; nara 
in hoc cafu i — pp:=.^ — ^ effet qu.intitas negativa , adeo- 
q 
ue 
