— 5—
§. 9. Ex hac aequatione EdE= 0 quatuor alias aequationes deducere possumus, quarum ope valores a, 6, ꝙ et w quantitatibus ex observationibus notis exprimuntur. Etenim AE d E nullo modo= 0 fferi potest,
nisi numeri coefficientes differentialium singulorum d„, do, d v, d 6 ipsi sint= 0. Ergo si, brevitatis causa, columnas hujus aequationis numeris romanis, quibus inscriptae sunt designamus, habemus: (I.)+(II.)*†(III.) †(IV.)= 0 (V.)+(VMI.)+(VII.) †(VIII.)= 0 (IX.)*†(X.)(XI.)(XII.)— 0 (NXIII.)+† XIV.)+† XV.)+†(XVI.)= 0. §. 10. Terminus(I.) i. e. ba cos+ba cos(450+)— ba sin— ba sin(450+ 4)— ba cos(450+† 9) + ba sin+ ba sin(450+†„) etiam hoc ordine scribi potest: ba cos— ba cos+† + ba cos(450+† †)— ba cos(450+„)— — ba sin&+† ba sin— — ba sin(450+ †)+† ba sin(450+†„), quo constituto evidenter apparet eum esse= 0. Simili modo elucet etiam esse(II.)= 0, et(III.)= 0; si vero est(I.)= 0,(II.)= 0,(III.)= 0, ex aequatione(I.)+†(II.)+(III.)+(IV.)= 0 sequi- tur etiam esse(IV.)= 0. Habemus ergo — B a cos— Bxo α cos(450+ p)+ Bo a sin+ Bsoo a sin(45+ †) † 5 Bs cos+ Bsw a cos(450+)— Bw a sin— Baw« sin(45⁰°0+ 9)— sive omisso factore, omnibus terminis communi et ordine meliore constituto: (B,— Bx) cos+†(Bsw— Bxo) cos(450+)+(B”0— B) sin+(Bao— Bxw) sin(450+)= V.)= 0, sive adhibitis formulis notissimis cos(X+ y)= cos X cos y— sin x sin y et sin(X † y) — sin x cos y+ cos x sin y.
;(Bs— B) cos+(Bsw— Bxo)(cos 450 cos&— sin 45° sin)+
=(IV.)= 0.
+(Bo— Bw) sin+(Bso— Bxw)(Sin 450 cos+ cos 450 sin 9)—=(IV.)= de e hl)
§. 11.
Pergamus ad disquisitionem accuratiorem aequationis(§. 9.) secundae
(V.) †(VI.) E(VII.)+†(VIII.)= 0.
Facillime elucet esse(V.)= 0 nec non(VII.)= 0, quibus valoribus positis in aequatione data prodit (VI.)+†(VIII.)= 0. Est vero 3(sin ν+† cos 4²)+ a ſsin(450+ 9)²+ cos(45°+ 9)²] † 1=(VI) *(Sin„2 † cos„²)+ a lsin 450+ 9)?+ cos(450+ 9)2] id est a a a a=— 4a=(VI.). Invenimus porro (Bs B) sin+(Bsw— Bo) sin(450+ 9)+(Bw— Bo) Cos„—=(VIII.) —+†(Bxw— Bso) cos(450+ 9). 44
sive (Bs— B) sin 9+(Bsw— B o) sin 450 cos+ cos 450 sin)+†
=(VIII. †+†(B— Bo) cos+(Bxw— Bso) cos 45° cos— sin 450 sin 4) b)