Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Theorema
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40.
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Collectio ſpatiorum eſt ſumma terminorum huius progreſſionis arithmeticæ
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;
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<
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<
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progreſſio accipitur in inſtantibus, & ratio velocitatum vt ratio incre
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menti impetuum; vt conſtat ex dictis, & hæc ſequatur ſimplicem
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progreſſionem 1. 2. 3. 4. &c. </
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<
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minorum. </
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Theorema
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41.
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Hinc cognito primo termino, & vltimo, id eſt ſpatio quod per curritur primo
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inſtanti & ſpatio quod percurritur vltimo instanti, cognoſcitur ſumma, id eſt
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collectio ſpatiorum, id eſt, totum ſpatium confectum.
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v.g.ſi primus terminus,
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ſecundus S.igitur ſumma eſt 36. quippe vltimus terminus indicat nume
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rum terminorum, quia primus eſt ſemper vnitas, & progreſſiuus etiam
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vnitas. </
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Theorema
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42.
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Hinc cognita ſumma & vltimo termino cognoſcitur etiam numerus inſtan
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tium æqualium, qui ſemper est idem cum numero terminorum, cognoſcitur
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etiam primus terminus, id eſt ſpatium quod primo instanti percurritur, cogno
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ſcuntur etiam gradus velocitatis
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; </
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<
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ne; </
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<
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quæ lubens omitto; </
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<
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">tùm quia Phyſicam non ſapiunt, tùm quia hypothe
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ſis illa eſt impoſſibilis phyſicè; quis enim ſenſu percipere poſſit & di
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ſtinguere vnum temporis inſtans, vel ſpatij punctum? </
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<
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id
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fuerit hæc accelerati motus proportio in inſtantibus, vt ad ſua phyſica
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principia reduceretur. </
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Theorema
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43.
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Data ſumma progreſſionis huius ſimplicis, inuenietur numerus terminorum,
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ſi inueniatur numerus, per quem diuidatur, qui ſuperet tantùm vnitate du
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plum quotientis
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; </
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<
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id
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rum v.g. ſit ſumma 10. diuiſor ſit 5. quotiens 2. duplus 4. hic eſt nume
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rus terminorum datæ ſummæ; </
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<
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">ſit alia ſumma 21. diuiſor ſit 7.quotiens 3.
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numerus terminorum 6. ſit alia ſumma 36. diniſor ſit 9. quotiens 4. nu
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merus terminorum 8. ſit alia ſumma 45. partitor ſit 10. quotiens 4 1/2,
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numerus terminorum 9. quomodo verò hic partitor inueniri poſſit, vi
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derint Arithmetici; </
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<
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huius progreſſionis ſimplicis facilè cognoſci poteſt numerus termino
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rum; duplicetur enim, & radix 9. neglecto reſiduo dabit numerum ter
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minorum v.g. ſit ſumma 21. duplicetur, erit 42. rad. </
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<
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terminorum; ſit ſumma 36. duplicetur, erit 72.rad.9.8. dabit numerum
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terminorum. </
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Theorema
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44.
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Semper decreſcit proportio incrementi velocitatis, id est maior est proportio
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velocitatis ſecundi inſtantis ad primum quàm tertij ad ſecundum, & maior
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