Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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vt lineæ. </
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<
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id
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">Hinc acquiritur velocitas æqualis, vt dictum eſt Th. 20. quia
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ſi tantùm addit tempus per AF ſupra tempus per AE, quantum addit
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motus per AE ſupra motum per AF, haud dubiè eſt æqualitas. </
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Theorema
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24.
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Hinc poteſt determinari longitudo plani, quæ dato tempore percurratur,
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v.
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g. perpendicularis 3. pedum percurritur 30tʹ. </
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<
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">igitur ſi aſſumas planum
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inclinatum 6. pedum, percurretur 1″. </
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<
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<
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<
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">atque ita dein
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ceps; </
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<
s
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">hinc poſſet dari planum inclinatum quod tantùm 100. annis per
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curretur, ſcilicet ſi longitudo plani aſſumpti ſit æque multiplex longitu
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dinis 12. pedum atque 100. anni vnius ſecundi; quod facilè eſt, imò da
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to plano cuiuſcunque longitudinis, poteſt dari tempus quodcunque quo
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percurratur, de quo infrà. </
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Theorema
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25.
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Determinari poteſt quantum ſpatium conficiat mobile in plano inclinato;
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dum conficit perpendicularem
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; </
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ducatus, EB perpendicularis in AC; </
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<
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">dico quod eodem tempore percur
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ret AE & AB, quod demonſtro; </
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<
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">quia triangula EAB, EAC ſunt pro
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portionalia: </
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<
s
id
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">igitur AB eſt ad AE vt AE ad AC; </
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<
s
id
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">igitur motus in AB
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eſt ad motum in DE vt AB ad AE; </
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<
s
id
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">igitur ſi tempora aſſumantur æqua
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lia ſpatia erunt vt motus, vt patet, id eſt motu ſubduplo acquiritur ſpa
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tium ſubduplum: </
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<
s
id
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">nec alia eſſe poteſt regula tarditatis, igitur ſpatia
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erunt vt AB ad AE, id eſt in ratione motuum; </
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<
s
id
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">licèt enim motus veloci
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tas creſcat, attamen ſi accipiatur velocitas compoſita ex ſubdupla maxi
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mæ & minimæ, percurretur AE motu æquabili æquali tempore; ſed
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compoſita ex ſubdupla maximæ & minimæ per AB habet
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ra
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tionem ad priorem compoſitam, quàm motus per AB ad motum per AE.
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& hic quam habet AB ad AE. </
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<
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id
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Theorema
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26.
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Hinc æquali tempore deſcendit per inclinatam BE,
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ſit enim inclinata
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AG, perpendicularis AE; ſit quoque FC perpendicularis in AG, & FD,
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in CF. </
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">Dico quòd eo tempore, quo conficit CD perpendicularem
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conficit CF inclinatam per Th.24. eſt enim DF perpendicularis in IC.
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ſicut FC in AG, ſed CD eſt æqualis AF, vt patet. </
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Theorema
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27.
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Hinc cognito ſpatio quod percurritur in plano inclinato, cognoſcitur ſpa
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tium quod conficeretur tempore æquali in perpendiculari,
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ſit enim tempus
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quo percurritur AC; ducatur ex C perpendicularis CF. </
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<
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">Dico confici AF
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in perpendiculari eo tempore, quo percurritur AC: </
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<
s
id
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">vel ſit inclinata C
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F, ducatur ex F perpendicularis FD; percurretur CD eo tempore, quo
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percurritur CF, quæ probantur per Th.24.& 25. </
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