Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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MATHEMATICA. LIB. I. CAP XIX.
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bemus ergo etiam demonſtratam propoſitionem in n, 386. </
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<
s
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">Supereſt ut, quæ de evolutione Cycloidis in n. </
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<
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ſtremus.</
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<
s
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xml:space
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">Detur iterum eadem Cycloïs ADB; </
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<
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micirculus. </
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xml:space
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<
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que parallelogrammo AfCF; </
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<
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">detur ſemicirculus A mf, qui ſemicirculo FEB,
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æqualis erit; </
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<
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<
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eſt ſemi-cycloïdi ADB. </
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C q A applicatum, evolvi.</
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<
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">Ponamus filum ad hunc perveniſſe ſitum, ut cum cycloïde tantum con-
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veniat à C ad q, & </
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linea q Q æqualis ſit arcui q A, cui filum, nunc tenſum, fuit applicatum, e-
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rit Q fili extremitas.</
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<
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">Ducatur q p ad baſin parallela ſemicirculum A m f ſecans in m, ex quo
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puncto ducatur linea m A ad A, ſunt m A & </
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<
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ſed q A, ideoque q Q dupla eſt m A aut qN; </
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<
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<
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ergo etiam erunt æquales arcus FM, A m; </
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El. III.</
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& </
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<
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lelogrammum, & </
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in parallelogrammo m AN q.</
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<
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">Linea mq, aut AN, æqualis eſt arcui A m , aut arcui FM; </
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<
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qualis eſt ſemicirculo FMB ; </
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<
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">idcirco NF, aut QM, æqualis eſt
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MEB, & </
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">punctum Q, ideſt fili extremitas datur in cycloïde ADB ,
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integram extremitas hæc percurret dum totum filum evolvitur.</
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<
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per arcus circuli exiguos breviori tempore deſcendere, quàm per ho-
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rum arcuum chordas. </
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ſcendit, quando puncta ambo non in eadem verticali dantur, ut viam ſuam
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breviſſimo tempore peragat, non debere per lineam rectam incedere. </
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nam autem lineam ſequi debeat, lubet hìc demonſtrate; </
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niunt quæ in ſuperiori ſcholio de Cycloïde demonſtrata ſunt.</
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<
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tendat ad B; </
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fig. 6.</
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citate quam dicimus v, ubi autem tranſivit lineam hanc incedat celeritate
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majori quam vocamus c: </
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rectas vias percurrere; </
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peragrare: </
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<
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omnium breviſſimo perveniat ex A in B,</
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<
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">Ponamus tempus quo corpus, velocitate v, lineam quamcunque percur-
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rit ipſâ lineâ percurfâ repræſentari; </
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te aliâ majori, eo brevius eſt, quo velocitas major eſt, & </
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ne in qua velocitas augetur; </
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tate c percurritur, repræſentabitur lineâ minore ipſâ percurſâ, & </
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ſam habet rationem quæ datur inter v & </
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<
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