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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 270, page id 1066518432:0298
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270 DE VTRIBUS ET MIOZIBUS CORPORUM. L1B. II.
PROPOSITIOLII. LPMMA.
468. Si recta AM positione datae alia AB magnitudine data perpen-
diculariter insistat, per cujus terminum B rectae quaecunque BM, Bm
ad alteram AMI ducantur, e per puncta M, m, SEC. in quibus huic
occurrunt; perpendiculares MN, mn, eC. ipsis BM, Bm, eC. re-
spective aequales, omnia puncta H, n, etc. in curva L. Nn hyperbolae
aequilatera sita erunt, cujus centrum A, e semilatus transversum
AL.
Fi8. X18. Positisque punctis M, m indefinite vicinis, ac descripto centro B in-
tervallo BM arculo Mu, junctisque ANT, An, rectanculum (ub radio
BA e arculo Me dupbum erit trilinei AVn seu elementi sectoris hy-
perbolici ANL.
T. DuCatE NX parallela AM, ec quia (secundum hypothesin)
MIN = BM, C AB = AL, CrIt AX =XNI2 + AL, vel XN2= AX
ANV =rCC. IO BXL, ergo punctum N est in lrperbola aequila-
tera LNY, cujus latus transversum cA BL. ex centrum A. C UEVa L N
etiam hyperbola erit, (i M N ad BM fuerit in quacunque data ra-
TiOne.
TI. Per punctum N ducta sIC tangens hyperbolx Ng, cruntque
ErES MIN vel BMI, AI vel BA e Ag in continua rationc, atque
adeo BMI: BA = BA: Ag, atqui propter criangula similia ABM e
A.Nm, est etiam BM: BA = Mm vel NO: MIp; ergO NO: MN =BA:
A9, acque adeo BA. MIp = LIo. A9 (num. IV. 3. 464.) =2. AIn.
Ouod crat demonstrandum.
C OROL L A R L U _ I.
469. Adeoque, E tOta AMI infinitis composita sic particulis infi-
nitesimis qualis NIm, ex per singularum terminos rectae BM ductxe
intelligantur, erit factum ex omnibus arculis Mu, quos ricinae quae-
que BM incercipiunt, ex radio BA aequale duplo omnium triangu-
lorum AAm quae in sectore hyperbolico ANL. continentur, id est,
duplo ipsius lectoris.
C OR OL L A R FU N II.
470. Ducendo igitur per punctum interfectionis + rectae AN et
tansentis hyperbola At in vertice, lineam isr parallelam AL, et
USL.