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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 13, page id 1066518432:0041
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DE VFREBAS ET MIOTTBUS CORPORUM. LTB. T. 13
AMI: AB SICUE AD ad AB, rerum ex trigonometria constat, esse
AD ad AB, ue sinus anguli ABD ad sinum anguli BDA, ergo
etiam AM est ad AB ut sinus anguli ABD, vel ejus supplementi ad
duos rectos BAC ad sinum anguli BDA, vel ejus alterni aequalis
DAC, aut etiam hujus ad duos rectos supplementi MAC. RE SIC
ex ternis solicitationibus, ad aequilibrium compositis, duxe quae libet
Cunt inter se uE Sinus angulorum ipss OpDOTItOrum, hoc eA AB:
RC = SIN. MIAC: SIn. MAB, _E AM: AC =SIM. BAC: SIn. MAB.
Et SiC ubique.
Elegans hoctheorema a Cel. Petro Varignon primum, quod sciam,
demonstratum est, cui ferme totam suam noram Mechanicam, dn-
n0 1687. Lutetixe cditam, superstruxit.
C OR OL L A R E U M TTI.
43. F.X hisce etiam patet ratio cheorematis non inelegantis, quod
Roberrallius Forricellio quondam provoluir, sed sine demonstra-
tione, ut ridere est in Opere Academia Resiae Scienciarum Pari-
Siensis, quod inscribitur Divers Ouoraces de Mathematique ex de Phy-
sique de Messieurs de l’Academie Royale des sciences, Fol. 301. Theo-
rema vero nostris loquendi phralibus exprestum, est hujusmodi: Si
per terminos rectarum AM, AB, AC trium solicitationum cidem
puncto a applicatarum, repraesentatricium, ducantur rectae MB,
BC _ MC, punctum A, cui Colicitationes in aequilibrio consisten-
tes impresae lunt, existet in centro graricatis triansuli MBC. Circa
AM, AB _ AM, AC descripta sint parallelogramma AMSB,
ARMC, quibus delcripris, et quiatres folicitationes AM, AB, AC in
aequilibrio sunt, secundum hypochesin AC ae quipollebit (5. 36.) ipsIs
AMI _ AB acgue adeo (S. + T.) AC = AS, et hae duxe in directum positx
erune, unde CA producta latus trianguli MB sccabit in medio
similiter AB producta secabit latus trianguli MC in ejus medio P;
jam ex Caticis constat triansuli MBC centrum graritatis esse in
singulis lineis C. BP ex quibuoris trianguli angulis C ex B ad
Duncta ec P in medio laterum BM ac CM angulis illis oppoli-
torum ductis, propterea centrum graritatis criansuli BMC, es in
communi intersectione a harum linearum CO) de BP.
PROPOSITIO IV. LF, M ne A.
44. Si singula corpora positione data A, B, C, D etC. in suam quod-
que