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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 252, page id 1066518432:0280
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252 DE VTRIBUS ET MOTIBUS CORPORUM. L. IB. II.
est triangulum, cujus basis etiam Pp, Sed altitudo dupla ip sius pP, seu
diametro L.MI aequalis; atque adco ejusdem alticudinis cum trian-
sulo L. An: ex angulus NLn =angulo (modo nominati trianguli)
ad verticem in circumterentia alterius lemicirculi in Agura non ex-
pressi; ergo Nn: Pp = NV: LM =NL: PL =LM: LR. Fodem
argumento cst O0: g =LM: IS, seu invertendo 1g: 10. vel
N = LS: LM; ergOCx aequo Og: Pp = LS: LR. Sed proptertrian-
sula similia 2gp ec T9S, est Ss vet o: 19 = 15: VI, ergo ex
xquo Ss: Pp = LS. QS: LR. OT. Item propter criangula similia
PPR, TPR est Pp: PF Vel RV = PT Vel OT: PR = LR. OT: LR.
PR, Crgo denuO Cx aequO HE, Ss: Rr = LS. OS: LR. PR; atqui
supra (nuM. FF. in AnC) invenimUS. Ss: RY = FB: Ba, erBO FB: La =
LS. OS: LR. PR, _ La. L5. OS = FB. LR. PR.
IV. Igitur, Si dicantur LM, a; Ea, e; FB, fe MO, M; quar-
ta provortionalis MZ ad dataS BHL, HIA eC L. M dicatuE S3 et RXC
vel MZ deprehendetur esse media arithmetica inter incognitas
MO _ NN, unde cum MO EEm, altera MN invenietur = 28 = m.
Et substitutis his raloribus in canone paulo ante reperto La. L5.
25= LB. L.R. PK, Perremetur ad aequationem quinque dimensio-
num, quae, Calro calculo, erit uc sequitur:
+ eM - 8eG. M + 24 e8G. m = 8aaZC. Mm + a C. M. = 2a+ f9 = 0.
+f
256 + 29af
+2aa0.
-49a58
= 328
+ 225
+ 168 e
- 8aae88
Cujus radices determinant valores quaesIEX MO; qua inventa du-
ataque OL, Si per datum punctum A duCetUT AC parallela ipA OL,
quae AC ocCurrat rectae CI, ei occurret in optato puncto C. Ouod
erat inreniendum.
Fxiisset pariter aequatio 5. dimensionum, si rel maxime lineas CC
ee BI inaequales atumpsisemuS.
C, OR OL L A R L V M I.
4N): LN CanONC SUPra in VeNTO La. LS. OS = FB. LR. PR jam COnEI-
netur solutio problematis de solido minima resistentiae. HIoc enim ca(u
CC _ BIperinde ac AC _ CT supponendae lunt indefinite parree, quo
ACL, ut aF _ AD, item BF ex CF. instar aequalium tractari debcant;
ec cum omnia Colica Lu. Ld. 9d; EB. L R. PK, dc. sinsula scilice
CuF-