347295SUPPLEMENTA. §. V.
earum directiones, adeoque RC, NC ipſis æquales, &
paral-
lelæ expriment vires illas tertiam, & quartam puncti C. Pro-
ducantur autem DC, AC, donec occurrant in O, & T re-
ctis ex N, & R parallelis ipſi CF, ſive ipſis GAZ, KDX,
& demittantur AF, DE, NQ, RS perpendicula in ipſam
FC productam, qua opus eſt, quæ occurrat rectis AB, DB
in V, P.
lelæ expriment vires illas tertiam, & quartam puncti C. Pro-
ducantur autem DC, AC, donec occurrant in O, & T re-
ctis ex N, & R parallelis ipſi CF, ſive ipſis GAZ, KDX,
& demittantur AF, DE, NQ, RS perpendicula in ipſam
FC productam, qua opus eſt, quæ occurrat rectis AB, DB
in V, P.
90.
Inprimis ob ſingula latera ſingulis lateribus parallela erunt
11Vires ſub nova
expreſſione in-
de reſultante. ſimilia triangula IAG, CTR, & triangula MDK, CON.
Quare erit ut IG, ſive AH, ad CR, ſive NB, vel AXAH,
nimirum ut 1 ad A, ita AG ad TR, & ita AI ad TC.
Erit igitur TR æqualis GA, ſive AZ ductæ in A, & CT
æqualis IA ductæ in A: adeoque illa exprimet ſummam om-
nium virium AZ omnium punctorum in A, hæc vim illam
primam puncti C, nimirum AXIA. Eodem prorſus argu-
mento, cum ſit MK, ſive DL ad CN, ſive RB, vel
DXDL, nimirum 1 ad D, ita DK ad ON, & ita DM
ad OC; erit NO æqualis KD, ſive DX ductæ in D, &
OC æqualis MD ductæ in D, adeoque illa exprimet ſummam
omnium virium DX omnium punctorum in D, hæc vim il-
lam ſccundam puncti C, nimirum DXDM. Quare jam erunt
Summa virium parallelarum in A - - - - - - - TR
Summa virium parallelarum in D - - - - - - - NO
Binæ vires in B - - - - - - - - - - - BN, BR
Quatuor vires in C - - - - - - CT, OC, RC, NC
11Vires ſub nova
expreſſione in-
de reſultante. ſimilia triangula IAG, CTR, & triangula MDK, CON.
Quare erit ut IG, ſive AH, ad CR, ſive NB, vel AXAH,
nimirum ut 1 ad A, ita AG ad TR, & ita AI ad TC.
Erit igitur TR æqualis GA, ſive AZ ductæ in A, & CT
æqualis IA ductæ in A: adeoque illa exprimet ſummam om-
nium virium AZ omnium punctorum in A, hæc vim illam
primam puncti C, nimirum AXIA. Eodem prorſus argu-
mento, cum ſit MK, ſive DL ad CN, ſive RB, vel
DXDL, nimirum 1 ad D, ita DK ad ON, & ita DM
ad OC; erit NO æqualis KD, ſive DX ductæ in D, &
OC æqualis MD ductæ in D, adeoque illa exprimet ſummam
omnium virium DX omnium punctorum in D, hæc vim il-
lam ſccundam puncti C, nimirum DXDM. Quare jam erunt
Summa virium parallelarum in A - - - - - - - TR
Summa virium parallelarum in D - - - - - - - NO
Binæ vires in B - - - - - - - - - - - BN, BR
Quatuor vires in C - - - - - - CT, OC, RC, NC
91.
Jam vero patet, ex tertia R C, &
prima CT com-
22Vis in ſulcrum
cui æqualis. poni vim RT æqualem ſummæ virium parallelarum A; & ex
quarta NC, ac ſecunda OC componi vim NO æqualem
ſummæ virium parallelarum in D. Quare patet, ab unico
puncto C fulcrum urgeri vi, quæ eandem directionem habeat,
quam habent vires parallelæ in A, & D, & æquetur earum
ſummæ, nimirum urgeri eodem modo, quo urgeretur, ſi om-
nia illa puncta, quæ ſunt in D, & A, cum his viribus eſſent
in C, & ſulcrum per ſe ipſa immediate urgerent.
22Vis in ſulcrum
cui æqualis. poni vim RT æqualem ſummæ virium parallelarum A; & ex
quarta NC, ac ſecunda OC componi vim NO æqualem
ſummæ virium parallelarum in D. Quare patet, ab unico
puncto C fulcrum urgeri vi, quæ eandem directionem habeat,
quam habent vires parallelæ in A, & D, & æquetur earum
ſummæ, nimirum urgeri eodem modo, quo urgeretur, ſi om-
nia illa puncta, quæ ſunt in D, & A, cum his viribus eſſent
in C, & ſulcrum per ſe ipſa immediate urgerent.
92.
Præterea ob paralleliſmum itidem omnium laterum ſi-
33Proportio, quæ
vectem exhibet. milia erunt triangula 1. ° CNO, DPC: 2. ° CNQ, PDE:
3. ° CPR, VCN: 4. ° CRS, VNQ: 5. ° CVA, TCR:
6. ° VAF, CRS. Ea exhibent ſequentes ſex proportiones,
quarum binæ ſingulis verſibus continentur.
33Proportio, quæ
vectem exhibet. milia erunt triangula 1. ° CNO, DPC: 2. ° CNQ, PDE:
3. ° CPR, VCN: 4. ° CRS, VNQ: 5. ° CVA, TCR:
6. ° VAF, CRS. Ea exhibent ſequentes ſex proportiones,
quarum binæ ſingulis verſibus continentur.
ON.
CP:
:NC.
PD:
:NQ.
DE
CP.
CV:
:CR.
NV:
:RS.
NQ
CV.
RT:
:VA.
RC:
:AF.
RS
Porro ex iis componendo primas, &
poſtremas, ac demendo
in illis CP, CV; in his QN, RS communes tam antece-
dentibus, quam conſequentibus, ſit ex æqualitate nimirum per-
turbata ON. RT: :AF . DE. Nempe ſumma omnium
virium parallelarum in D, cui æquatur ON, ad ſummam
in illis CP, CV; in his QN, RS communes tam antece-
dentibus, quam conſequentibus, ſit ex æqualitate nimirum per-
turbata ON. RT: :AF . DE. Nempe ſumma omnium
virium parallelarum in D, cui æquatur ON, ad ſummam