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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 245, page id 1066518432:0273
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DE VLRTBUS FT MOTZBUS CORPORUM. L. IB. II. 245
IVo. Flae postremx nullo negotio ex secunda eliciuntur, substituen-
do duntaxat loco a ec m elementa proportionalia dy et dx. Tam oDC
harum quatuor aequationum generalium raria problemata solvi pol-
sunc, quorum nonnulla proponere libet.
PROPOSETIOZEV. PROBLEMA.
438. Assienare proportionem inter resistentias, quas trianculum isosce. F18. 2XY:
les BE. R in puido patietur, si, ut in praecedente, modo basi BR, modo ver-
tice F directione AV in id feratur.
Fxstructo super dimidia bali AB quadrato, AM demittatuE CX A
perpendicularis AF ad latus trianguli EB, ee per punctum Faga-
CuF FC parallela axi F A, ex facta AI vel BHI aequali BC, crit rC-
eta TII Icala resistentiarum linex F B, critque adeo resistentia linex
EB ad relistentiam linex BA ut rec lum BI ad rec- lum BP, Pcu ut
AIad AP; acque adeo in duplicata ratione lincae F. B ad BA, vel a9-
sregati laterum BE _E PR ad basin BR crianguli ilo(celis BRR;
atqui, ut resistentia lincae FB ad resistentiam linexe BA, ita resisten-
tia lincarum BF, RE Timul, seu totius trianguli, praecedente ejus ver-
ticcE, ad relistentiam basis BR, ergo harum resistentiarum ratio x-
quiralet duplicata rationi laterum BF, RP ad balin BR. Nam, (I
BA reprXlentet quadratum celeritatis trianguli, BC vel AI (5. 4. 35.)
exponet ordinatam constantem scalae resictentiarum FII trianguli,
vel pocius linex rectae patientis BF. Ouod erat inveniendum et de-
monstrandum.
oroRLaM I.
439. Adeoque resistentia quadrati, juxta directionem lateris II
Auido delati, erit ad resistentiam ejusdem, sed in directione diagona-
lis pari celeritate incedentis, ut diameter quadrati est ad latus ejus-
dem. Nam si triangulum ilolceles BFR cogitetur rectangulum esse
in F, erit (5. 438.) relistentia laterum BF, FR juxta AF, ad resi
sentiam basis BR, quae diameter est quadrati cujus triangulum BF. R
eAt semissis, ut AI ad AP, Ieu BF ad BE; resistentia vero diametri
quadrati BR perpendiculariter incedentis super AF, eA ad relisten-
tiam lateris quadrati BP. itidem normaliter super AF delati, SICUE
BR ad BE sCu 2BA ad BR, sCu 2BF ad BR, id eAt BF. ad BA; Cr-
B0 ex aequo resistentia laterum BF.R, seu quadrati, juxta directionem
Ih 3
dia-