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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              <s id="N169EB">Cùm enim ratio ſpatiorum ſit vt ratio velocitatum; </s>
              <s id="N169EF">dum ſcilicet hæc
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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. </s>
              <s id="N169F9">certè collectio ſpatiorum eſt ſumma ter­
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              minorum. </s>
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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. </s>
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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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              ; </s>
              <s id="N16A3F">quippe hæc omnia ſunt in eadem ratio­
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              ne; </s>
              <s id="N16A45">quæ omnia conſtant ex regulis arithmeticis præter alia multa data,
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              quæ lubens omitto; </s>
              <s id="N16A4B">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? </s>
              <s id="N16A53">licèt recenſenda
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              fuerit hæc accelerati motus proportio in inſtantibus, vt ad ſua phyſica
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              principia reduceretur. </s>
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                <emph type="center"/>
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              Theorema
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              43.
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              </s>
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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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              ; </s>
              <s id="N16A77">quippe habebis in duplo quotientis numerum termino­
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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; </s>
              <s id="N16A81">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; </s>
              <s id="N16A8D">nec enim eſt huius loci, quamquam datâ ſummâ
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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. </s>
              <s id="N16A99">9. 6. dat numerum
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              terminorum; ſit ſumma 36. duplicetur, erit 72.rad.9.8. dabit numerum
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              terminorum. </s>
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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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              </s>
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