266 
Opuscula. 
ligere , lineas tres A B , B C , C D fufpenfas e pundis A , D , 
fi in xquilibrio confiilant, in uno eodem verticali plano 
iacere omnes , nempe in plano A K D . Neque cnim polfet 
verticale planum duarum B C , C D aliud eife a verticali 
plano duarum A B , B J , nifi fi reda B C , qua: media eil , 
verticalis ipfa foret ; qax fi verticalis elTet , non poifet pia- 
num B C D infra redtain B D eife conllitutum , ut clarun; 
per fe eii: . 
Verticales igitur linex RO,BQ^, SL,CE,TI (Fig.i.) 
per puada R, B , S , C , T duilx iiorizoatali D K occurrent in 
O , Q_, L , £ , I . Ex noto autem mechinicoru n theoremate 
ceiitmm commune gravitatis rediru n trium A 8 , B C , C D ab 
, . 1- j-i . • Af^.KOH-BC.SL-hCD.TI 
horizontali DK dutaDit quantitate ; 
^ ABH-BC-hCD 
qua propterea qu.iatitate maxi^num continetur. 
Per B & C fiat hoiizo jtales BG,CF, qux fecent ver- 
ticales AK, B Q__ in G k P; vo:encarqae re6tje graves 
AB , BC , CD a\ d\ anguii vero G AB, FBC, ECD 0, cp', cp". 
ex quo erit ~ a > cos cp , BF d» cos ^\ GE — d'- cos (^'\ 
& R O — d'- cos -1- d- cos {|3' -\- f_lf ^ S L — d'- cos (0' 
♦ cos 0^^ jj^f — S^JL. Fa6tis igitur fubllitutionibus in 
formula modo inventa, erit maximum 
^ u , , . ^.cosa? , „ d."os'o\ ^,a'''Coscp\ 
a{a .cos 9 -\-a .cos 9 H- )~\-a {a -cos (p -1 )-{-a ( ) 
2 
a-\-a-\-a 
Hinc per vulgarem maxiaiorum & minimorum methodum 
a{ — d''Cm cp'*' d — ^i^.fin qo'.^^' — ^^-^ — .'—)-\-d{—d''Cm p'' d 9'' 
.)-{-a ( —)—o. Sed a . cos :p -i-/^ -cos ^ 
2 2 
H-^.cos(p = AK eftquantitas cOnilans ; quare — a'' - findp" • d .p' 
— d'Cm ':r:''d o — a ' fm d - d p ~ o: & conftans etiam eft 
quantitas d'' fin (p''-\-d' Cm ■p -h a . fin — DE-f-CF-f-BG=:DK ; 
ex quo a''' cos T''d:p' -f- d' cos ^4)* \ -}- . cos - p =^ o . Ergo 
ehminando duo ex tribus elem :ntis d r <) d .\ d ^'\ tum divi- 
dendo fuperilitem xquationem per tertium , exGitet denique 
fin ( 9 — (jp ) • fin 9 ( ^ ' + ^") — fin (9' — >^") • fin :p • ( ^ -f- ) . 
Sint 
