III

--- z= a y -^ co^ — ay — c a .

ftp ' '

^^ " II. ri » If

-— = a y -h ex — av — ex.

(it/ ' '

'^^- = b'oi +a^' — hoL' —,rp.

dp

"^ A'>y'L •i'^" A/v" rf"^'

auiui- perpt'iidinius , valores difTerentialium fit. du sic- prcxli-uiitiuiii , iequales esM' «Ichcre, indepc'iidcnlcr a difTercntialibus dx, dy, quantitatibus Tc/.r — IVA . L d.r ->- Sdy w.su.. iiivcnuïiuus, post quasdani transforinatioiios salis obvias.

C'T -.^ aKb'V ■+- i5 B6'i'-H /Ci'/.'

— '2<x'\l>h'— 2^'Kbb'— .ly'Cbb' ->- a"kbb ■+- fi"Kbb -h y"Cbb.

en ^ - «Art'A' — ,5Brt'// — -/Crt7/

-.- a'A {ab'-h ba') - .3'B(«*' -4- />«') -i- y'Cki/.'- ha')

— x"\ah — fi"nab—y"Cah.

C'N = aAa'a'-;3Brt'rt'-(-/C'a'rt'

f k / fit fi I I i " '

— '2 X Aaa — 2 p luia — a y i..aa ^ x" Aaa -hjS'Brtrt -^ y"i\aa

— 5ai —

Si i laque, brcvitaiis causa, statuimus

(i) Aa -f- B/S -+- Cy = D,

fit

C'T = Di'i' — 2 D'iA' + D"4^,

C U = — Da'b' -h D' (ab' -f- 6a') — T)"ah, C«V = Da'a' — 2D'afl' + D"«fl.

Hinc invenimus , evolutione facta ,

C* (TV — UU) = (DD" — D'D') (ab' — ba'f — (DD" — D' D') CC ,

et proin formulam pro mensura curvalurse ,

, DP" — D'D'