Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              Theorema
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              49.
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            <p id="N16C5B" type="main">
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              In progreſſione arithmetica ſi diuidatur numerus terminorum bifariam æ­
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              qualiter nunquam ſumma poſterioris ſegmenti eſt tripla prioris
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              ; ſed ſi acci­
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              piantur duo termini eſt tantùm 2/1, ſi 4. eſt 7/3 ſi 6. eſt (15/6), ſi 8. eſt (26/10), ſi 10­
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              (40/15), ſi 12. (57/21), ſi 14. (77/28), atque ita deinceps. </s>
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            <p id="N16C6C" type="main">
              <s id="N16C6E">Ex quo obſerua mirabilem conſequutionem; </s>
              <s id="N16C72">quippe ſi aſſumantur
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              tantùm duo termini, & diuidantur bifariam, ſumma poſterioris medie­
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              tatis eſt tripla primæ minùs vnitate; </s>
              <s id="N16C7A">ſi accipiantur 4. eſt tripla minùs
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              2. ſi 6. minùs 3. ſi 8. minùs 4. ſi 10. minùs 5. ſi 12. minùs 6. ſi 14. mi­
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              nùs 7. atque ita deinceps; vnde ſumma poſterioris medietatis eſt ſemper
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              tripla minùs numero ſuorum terminorum, vel quod clarum eſt minùs
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              ſubduplo vltimi, ſeu maximi termini, vel numeri terminorum totius
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              progreſſionis, quod probè omninò tenendum eſt, vt omnes experientiæ
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              explica ri poſſint, quod infrà faciemus. </s>
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            <p id="N16C8A" type="main">
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                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              50.
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              </s>
            </p>
            <p id="N16C98" type="main">
              <s id="N16C9A">
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              Ex dictis hactenus facilè redditur ratio maioris ictus eiuſdem corporis im­
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              pacti quod cadit ex maiori altitudine
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              ; fuit hyp. </s>
              <s id="N16CA5">1. ſed ideò eſt maior ictus,
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              quia maior imprimitur impetus, vt patet, at ideò maior impetus impri­
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              mitur, quia maior eſt imprimens per Ax. 2. creſcit enim impetus, vt
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              conſtat ex dictis. </s>
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            <p id="N16CAE" type="main">
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                <emph type="center"/>
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              Theorema
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              51.
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              </s>
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              Hinc quoque ratio maximæ percuſſionis ex ſolo pondere cadentis illius arie­
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              tis inflictæ
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              ; quâ ſcilicet altè infiguntur lignei pali, quibus in mediis
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              aquis tanquam iacto fundamini ſuperædificatur ingens ſæpè ædificij
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              moles. </s>
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            <p id="N16CCD" type="main">
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                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              52.
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              </s>
            </p>
            <p id="N16CDB" type="main">
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              Hinc ex minima altitudine cadens corpus graue minimum ferè ictum in­
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              fligit
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              ; quia primus impetus valdè debilis eſt, qui tamen deinde facta
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              acceſſione maximus ferè euadit. </s>
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            <p id="N16CEA" type="main">
              <s id="N16CEC">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              53.
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              </s>
            </p>
            <p id="N16CF8" type="main">
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              Hinc ratio, cur tanta ſit differentia impetus grauitationis, & percuſſionis
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              ab eodem mobili
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              ; </s>
              <s id="N16D05">quia ſcilicet quantumuis tempore breuiſſimo mouea­
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              tur, plurimis tamen eius motus durat inſtantibus; atqui quolibet inſtan­
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              ti motus acquiritur impetus æqualis primo impetui grauitationis, vt
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              conſtat ex dictis. </s>
              <s id="N16D0F">v. g. ſit mobile quod moueatur per mille inſtantia
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              (modicum certè tempus & minimè ſenſibile) poſt hunc motum impetus
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              erit millecuplus; </s>
              <s id="N16D1B">igitur effectus etiam millecuplus; quæ omnia conſtant
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              ex dictis. </s>
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            <p id="N16D21" type="main">
              <s id="N16D23">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              54.
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              </s>
            </p>
            <p id="N16D2F" type="main">
              <s id="N16D31">
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              Hinc percuſſio quæ fit in primo inſtanti contactus creſcit vt tempus
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              ; </s>
              <s id="N16D3A">quia
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              cùm ſingulis inſtantibus creſcat impetus per partes æquales, & cùm per­
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              cuſſio ſit vt impetus; etiam erit vt tempus; </s>
              <s id="N16D42">igitur percuſſio, quæ fit poſt
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              duo inſtantia motus eiuſdem corporis grauis deorſum cadentis eſt du-</s>
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          </chap>
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