Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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PHYSICES ELEMENTA
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<
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<
s
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xml:space
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">Concipiamus dari vim, qua corpus, ubicunque detur, pellatur centrum
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xlink:label
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xml:space
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C verſus, non intereſt quomodocunque in punctis diverſis varietur vis
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fig. 2.</
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hæc; </
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<
s
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xml:space
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">concipiamus vim hanc non eſſe continuam, ſed illam ictibus in cor-
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pus agere, & </
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<
s
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xml:space
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">momenta temporis inter ictus eſſe æqualia. </
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<
s
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xml:space
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pus projectum per AB hanc percurrere lineam in momento tali; </
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<
s
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xml:space
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">motum
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per BL, æqualem AB, in momento ſequenti continuaret, niſi in B ictu
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in corpus pelleretur hoc ad C; </
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<
s
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xml:space
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">ponamus celeritatem, ex hoc ictu oriundam
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in corpore jam agitato, talem eſſe, ut hac corpus poſſit, in intervallo tem-
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poris inter duos ictus, percurrere lineam LD; </
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<
s
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xml:space
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">ſi LD ſit parallela BC,
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corpus duobus motibus agitatum pecurrit BD , daturque in D, in momento
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quo ictu ſequenti iterum ad centrum pellitur. </
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<
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xml:space
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">Si ictus hic non daretur, in mo-
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mento ſequenti percurreret DE, poſitis DE & </
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<
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xml:space
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">BD æqualibus, ſed eodem
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tempore centrum verſus fertur, id eſt per DC pellitur, ſi juxta hanc dire-
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ctionem percurrat lineam æqualem lineæ EF in tempore in quo percurre-
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ret DE, motu compoſito corpus movetur per DF, poſitis EF & </
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<
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rallelis. </
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<
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xml:space
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">Eodem modo demonſtramus in momento ſequenti corpus percur-
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rere FH, ſi GH ſit æqualis ſpatio in hoc momento, ex ictu C verſus per-
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currendo, poſitiſque FG & </
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<
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<
s
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xml:space
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">Triangula ABC, BLC, habent baſes æquales AB, BL in eadem li-
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nea, & </
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<
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<
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<
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">Triangula
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BDC baſinhabent communem BC& </
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<
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">conſtituuntur inter parallelas BC, LD,
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ſunt ergo æqualia . </
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<
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xml:space
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">Idcirco etiam æqualia ſunt triangula ABC, BDC.</
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<
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<
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xml:space
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">37. El. 1.</
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Eodem modo demonſtramus æqualia triangula BDC, DFC & </
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<
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re æqualia eſſe inter ſe triangula quæcunque ut ABC, BDC, DFC;
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</
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<
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">FHC, quorum baſes momentis æqualibus a corpore projecto percurrun-
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tur. </
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<
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xml:space
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<
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<
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<
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">vi centrum verſus tendenti agitatum, move-
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ri in plano, quod tranſit per lineam juxta quam corpus projicitur & </
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<
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virium, ut monuimus in n. </
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<
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<
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<
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">Concipiamus nunc momenta inter duos ictus minui, ut & </
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<
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">ipſos ictus, ma-
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<
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">396.</
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nentibus nihilominus illis æqualibus inter ſe, poſitis hiſce utcunque inæ-
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qualibus, demonſtratio eadem locum habebit. </
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<
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">Si diminutio ſit in infinitum
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mutantur ictus in preſſionem continuam, & </
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<
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">corpus in ſingulis punctis a via
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recta deflectitur; </
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<
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minata. </
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<
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xml:space
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">Si ergo corpus moveatur in curva ABDE, & </
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<
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<
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fig. 11.</
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tur diviſum in momenta infinite exigua, & </
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ACB continebit tot triangula exigua æqualia inter ſe, quot dantur momen-
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ta in tempore, in quo percurritur AB, & </
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<
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dem modo continebit tot triangula æqualia inter ſe & </
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<
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tur momenta in tempore in quo percurritur DE; </
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<
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corpus AB & </
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<
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">DE, percurrit, ſunt inter ſe ut numeri triangulorum æqua-
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lium areis ACB, DCE, contentorum, id eſt ut ipſæ areæ. </
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<
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lem deducimus propoſitionem in n. </
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<
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<
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<
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<
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</
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Si corpus motum per AB in momento ſequenti, & </
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<
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">æquali, percurrat BD, quia
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<
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fig 2.</
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