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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 272, page id 1066518432:0300
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272 DE VFRTBDS EF MIOTEBOS CORPOROM. LTB. II.
ostensum sIE, Ck eNe ad fh ut tenacitas fili in elemento Cc, ad
hoc elementum CC, vel permutando Ck ad dictam tenacitatem ut
Th ad CC; Crit V2. ce: V AB = ce: AB = fh: CC, _ permutando ce:
fh = AB: CC.
TT. Per terminum B datae BA ducantur BMI, Bm Parallelae cle-
entis CUITVX CC, C0, centroque B interrallo BI) =C( = C6
delcripto arculo R, agantur 9S, Ro parallelae AM, item RX
aequidistans BA; S I perpendicularis ipsi BC, et denique TV pa-
ratsela S quibus politis, ultro liquet, triansulum BOS triangu-
I0cCf, et BRo triangulo CCF similia, aequalia, et similiter polIta
eNC; adeo uE SInE aO = fh, BV =CC, _ CC =B( vel BR; 2dco-
que analosia praecedentis numeri ce: fh = AB: C6, eadem est cum
BV: ∞O = AB: BQ; in triangulis vero rectangulis similibus jOR
_ BTS, bales y e BS a perpendiculis Ra _ TV proportiona-
liter diridentur, adco ut sIE a: γO = BV: BS, ec permutando ac
inrertendo BV: XO = BS: VO = BA: Mm; antea vero habuimus
BV: aO = AB: BQ; ergo etiam AB: MIm = AB: BO, atque adeo
NIm = BO =Cc; quod cum de lingulis Mm, guxe in tota Am et de
singulis Cc, quae in tota curra cCrA continentur, respectire raleat,
Liguet omnes NIm, PCU FOtam Am vel AM omnibus CC, PCu FOti CCT A
vel CCA aequari. Onde, quia BMI tansenti relarixe in puncto C
(secundum sirpothesin) parallela est, erit data BA ad AMI seu ipsI
aequalem curram ACC, sicut ordinata CI ad Cubtangentem vela-
rix respicientem ejus punctum C. Ilaec proprietas etiam catenarie
conrenit, ut alibi relarixe atque catenariae identitas jam (5. 106.)
Ostenta est.
TII. Constructio autem currae hactenus ex ostensis Facile elicie.
EUT: NAM CUM Nm (IE =CC, e Bm (secundum hypothesin) Paral.
Iela CC, descripto centro B arculo Mu, triangulum Mmu trian-
sulo cCf simile ex sequale erit, ac proinde Cf = m, d Omnes Cf,
id Cst, WV A = omnibus mu Ceu mi, descripto scilicet centro B radio-
que BA circulo A0. Sic etiam abscissa AI aequalis existet M0 pOsi-
ta, ut antea, BMI parallela tangenti currae in C.
Elementum rero ordinatxe cf =Mu _ omn. cf, Teu cWV aut CT =
omnibus MIp (5. 470.) = PO posita constructione in citato hoc pa-
rasrapho 470. EA erso qua libet ordinata CL aequalis homolosa
PO. Duae omnia crant invenienda.
O.