CAPUT V.

T72

unde fequitnr/*±eofi§

tang 2& —

Verum ex fuperiori ob tang zB =

2 E co/tj -s, zFfn

Acofo' + Bf n > - C+ z Uj\ ccjn *

2 tang B

habetur:

tang zB —

i — tang B 2^(Efti — Fcof n)((B— J)fy l cofy ] J r D (

(EJ'n - Fcofn) + V(cofn*-fn*)) z

quibus valoribus coaequatis erit

(Ecof n +Ffti) (Ef n - Feof„) ' - (Ecof n +Ff n ) ((«_ A)f n cofn+ D(coJY-fy z )) z

•\-(Efn-F ctfyj) (( B—A)fncofn-\-D(j:off —fn*')) (A cof-C+iDfqcofq )

- {{B - A)ft,cof i + D{tofn*-fi*)y (E(Bfr,-Cfy+Dcofri—F{A cofyi — Ccofi] -p D/■/}))

Cum jam fi n et cof n ubique totidem compleant dimenfiones, fi ponamusfi)

—y = tang tj — t, obtinebimus hanc aequationemc0 Jn

(E + F/) (.F - EO a = (D + (B _ A) t — D tt ) (DE-AF + CF +(BE - CE - DF)Y)quae in ordinem redatfia dat

o = EFF —DDE + (A-C)DF

+#(F*-aEEF + DDF + (A-aB + C) DE — (A — B) (A-C)F)+ (E } — a EEF-j-DDE -j- (ft — 3 A + C) DF+ (A-B)fB~C; E)+ t' (EEF —.DDF + (B - C) DEOita ut ex hac aequatione cubica valor ipfius t emi debeat.

COBOL L /,

439. Cum aequatio,, ex qua valor ipfius t inveniri debet, fit cubica,femper unam certe habet radicem renlem, quae praebet tangentem an-guli A 1 F = yj, quo angulo'invento alter FlG = B ita definitur ut fit 1{B^Ayfncofn + D (c< fn z -fn 21 ) _ i{B~A)fi 2n -\-Dcof 2^an& ~ Efm—Fcofn ~ Efn-Fcof n

C O R O L L. r.

440. Fieri autem potefi, ut omnes tres radices fintreales, quo«afu tres in corpctre dabuntur axes, quorum reipedu momenta inertiaefuut vel maxima vel minima.

SCHO -