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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 59, page id 1066518432:0087
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M
C
DE VERTDOS ET MIOTIBOS CORBORDM. L.1B. I. 59
ex F acquisitae erunt aequales distantiis punctorum à centro D posi
tis aequalious, celeritas que uniuscujusque mobilis poterit duplum area
AZBF A.
Totum spatium AF. in innuinera elementa, quale est Fe, diritum
cogitetur, X per lingulorum terminos arcus ex centro D delcripei
intelligantur; adeo ut singulis elementis rectae AE, cocidem clemen-
ta CurrX MOH relpondeant. Jam cum (5. 135.) ubique momen
cum celeritatis in currae puncto N aequetur momento celeritatis in
rectae puncto F, alteri N a centro D aequidistanti, habebitur lem-
per ec ubique (163 = 2Fl2628, ergo omnia ElC, quae in triansu-
lO TIAC continentur aequalia omnibus 2FI2628, qua in triangulo
2FI2A2C, id est triangulum FIACF trianoulO 2FI2A2C aequabItT.
Onde cum haec aequalia triangula similia line, sequitur lacera in il-
lis homologa aequalia eNe, atque adeo AC = 2A2C; id est celeri-
tates in L ex H acquilitae, quae per aequales 2A2C5 eE ACF exPO.
RUnEUT, dequales FUNE.
POrrO, quia (5. 132.) TIGE = BF. Ce e sic ubique, erunt omnia
HCe = omnibus BF. Fe, acqui omnia rec- la FIC componunetrian-
sulum HIAC, vel hAG, quandoquidem OtuS in A et MI punctis
nullus est, atque adeo etiam momenta celeritarum in illis punctis
nulla sune, id est cum criangulorum HIAC, _ 2II2AZC vertici
DuS A _ 2A confunduntur, ex in illis, ut ita dicam, nullelcunt: Om-
nia vero rectangula elementaria BFe, qua in EOFA arCA AALBR COn-
tinentur, huic arcae ultimo aequalia AUnE, aEque adeo arCA AAZ BH,
aequatur ubique triangulo homologo HAC, et duplum arex illius
duplo hujus trianguli, sed hoc trianguli duplum aequale cst qua-
drato lateris AC vel CHI, quoniam hoc criangulum rectansulum
isosceles est; ergo AC = 2. AASBB, vel quia AO aequalis est RF,
FF. = 2. AAZBE, id est celeritas in F, vel N acquisita potest du
DIIM AFCX AALBF. Oux omnia erane demonstranca.
C OR OE L A R Y U M I.
137. Pariter SI COrpOra A e M in curra ee recta ex punctis C
e Pccleritate aequali caltere incipiane, de quidem ea, quam mebi-
le A Spalt AF d Elllete perlabens in puncto P acquirere porcst;
eadem corpora in quibusris aliis punctis N et R, a centro Collicita-
tienum aquidistantibus, aequalem celeritatem acquirent, tantam sci-
licet quancam mobile A, in hoc puncto A casum a quiete in CID. CnS,
la PFu