Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              debunt 6. ſecundæ 12. igitur ſumma erit 18. minor vero ſpatio ſcilicet
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              21.hinc vides ſuppoſito eodem inſtantium numero ſpatium eſſe ſemper
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              æquale, ſiue aſſumantur partes maiores temporis, ſiue minores, v. g. ſup­
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              poſitis 6.inſtantibus, ex quibus totum ſpatium 21.conſequitur, ſiue aſſu­
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              mantur tres partes, quarum quælibet conſtet 2. inſtantibus, ſiue duæ,
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              quarum quælibet conſtet tribus, ſpatium quod ex illis reſultat, eſt ſem­
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              per idem ſcilicet 18. aſſumptis verò 8. inſtantibus, & totali ſpatio, quod
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              illis reſpondet 36. ſpatium quod ex partibus reſultabit erit 30. ſiue ſint
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              duæ partes, quarum quælibet conſtet 4. inſtantibus, ſiue ſint 4. quarum
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              quælibet conſtet duobus: </s>
              <s id="N16BA7">hinc rurſus vides aſſumpto maiori inſtantium
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              numero ſpatium verum habere maiorem rationem ad non verum, quàm
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              aſſumpto minori inſtantium numero, v.g.aſſumantur 4.inſtantia, ſumma
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              ſpatiorum erit 10. ſi verò aſſumantur 2.partes temporis, quarum quæli­
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              bet duobus inſtantibus reſpondeat; </s>
              <s id="N16BB3">ſumma ſpatij erit 9.igitur ratio ve­
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              ri ſpatij ad non verum eſt (10/9). aſſumantur 6. inſtantia ſpatij veri, ſumma
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              erit 21.non veri 18. igitur ratio (21/18) ſeu 7/6 quæ maior eſt priori: denique
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              aſſumantur 8. inſtantia ſpatij veri, ſumma erit 36. non veri 30 igitur ra­
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              tio (36/30) ſeu 6/3 quæ maior eſt prioribus, atque ita deinceps. </s>
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              Theorema
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              48.
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              Datis duabus partibus temporis, & cognito ſpatio quod percurritur in prima,
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              matius ſpatium reſpondebit ſecundæ quo vtraque in plures partes minores diui­
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              detur, ſuppoſita ſemper eadem progreſſione arithmetica in ipſo incremento
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              ; </s>
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              ſint enim duæ partes temporis ſenſibiles æquales AG. GH. & ſpa­
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              tium quod percurritur prima parte temporis AG ſit HI; </s>
              <s id="N16BE3">in ſecunda
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              percurretur IO, id eſt, duplum HI; </s>
              <s id="N16BE9">at verò diuidatur pars temporis
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              AG in duas æquales AF, FG, & conſequenter totum tempus AH in 4.
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              æquales; </s>
              <s id="N16BF1">haud dubiè in prima AF percurretur NP ſubtripla HI, & in
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              ſecunda FG percurretur PK dupla NP; </s>
              <s id="N16BF7">igitur in 4. partibus temporis
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              AH percurretur ſpatium decuplum PN, ſed HO eſt tantùm nonecupla
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              NP; </s>
              <s id="N16BFF">igitur reſultabit maius ſpatium in 4.partibus temporis, quam in dua­
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              bus; licèt duæ æquiualeant 4. iuxta progreſſionem arithmeticam. </s>
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              <s id="N16C07">Similiter AF diuidatur bifariam in E. & tota AH in 8. æquales AE; </s>
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              certè primis 4.percurretur idem ſpatium ML æquale NK & HI; </s>
              <s id="N16C10">igitur
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              in prima AE percurretur MR. cuius ML ſit decupla; </s>
              <s id="N16C16">nam 4. terminis
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              reſpondet ſumma 10. ſed 8. terminis id eſt 8.partibus temporis reſpon­
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              det ſumma; </s>
              <s id="N16C1E">6. æqualium RM; </s>
              <s id="N16C22">ſed HO tripla ML eſt tantum 30.
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              æqualium MR; igitur in 8.partibus reſultabit maius ſpatium, quàm in
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              4.quæ æquiualent 8. </s>
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            <p id="N16C2A" type="main">
              <s id="N16C2C">Ex quibus etiam conſtat quo plures accipientur partes temporis ma­
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              ius ſpatium reſultare, donec tandem perueniatur ad vltima inſtantia, ex
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              quibus reſultat maximum; </s>
              <s id="N16C34">& ſi accipias AG partes temporis AG. GH.
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              habebitur HO; </s>
              <s id="N16C3A">ſi verò 4.æquales AF, creſcet ſpatium ſeu ſumma 1/9 HO; </s>
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              ſi autem 8. æquales AE creſcet 1/5 HO; </s>
              <s id="N16C43">ſi porrò 16. æquales AD creſ­
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              cet (22/108) ſi 32. æquales AC creſcet (120/408); ſi 64. æquales AB creſcet (496/1584). </s>
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