Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              <s id="N284BD">
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              ſcilicet toto niſu applicata, ſit etiam longitudo AC dupla AB: </s>
              <s id="N284C9">dico
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              quod eodem tempore H acquiret æquale ſpatium ſcilicet CAD; </s>
              <s id="N284CF">igitur
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              CAD eſt 1/4 CAG, quia eſt æquale BAF; </s>
              <s id="N284D5">igitur CD eſt 1/4 CG, ſed
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              CG eſt duplus BF; </s>
              <s id="N284DB">igitur CD eſt ſubduplus BF; </s>
              <s id="N284DF">igitur velocitas ex­
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              tremitatis C in CA eſt ſubdupla velocitatis B in BA: </s>
              <s id="N284E5">adde quod AC cùm
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              numerus partium AC ſit duplus numeri partium AB, & cùm in eadem
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              proportione diſtribuatur impetus AC, & AB; certè partes maioris ſi
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              comparentur cum partibus proportionalibus minoris, ſubduplam tan­
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              tùm habebunt portionem. </s>
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            <p id="N284F1" type="main">
              <s id="N284F3">Sextò, ictus inflicti à malleis, quorum manubria diuerſam longitu­
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              dinem habent, ſuppoſito eodem angulo, ſunt vt longitudines; </s>
              <s id="N284F9">ſi enim
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              eo tempore, quo AB facit ſpatium BAF, AC facit CAD; </s>
              <s id="N284FF">certè æquali
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              tempore AC faciet DAG, vt conſtat ex natura motus accelerati; </s>
              <s id="N28505">
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              igitur acquirit
                <expan abbr="tantũdem">tantundem</expan>
              impetus; </s>
              <s id="N2850E">ſed eo tempore, quo AC decurrit
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              CAD, acquirit æqualem impetum AB dum percurrit BAF, vt patet ex
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              dictis; </s>
              <s id="N28516">igitur AC decurſo CAG habet duplum impetum AB decurſo
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              BAF; </s>
              <s id="N2851C">igitur dupla eſt vis ictus; </s>
              <s id="N28520">igitur ictus ſunt in ratione ſubdupli­
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              cata CAG, BAF; igitur vt ACAB. </s>
            </p>
            <p id="N28526" type="main">
              <s id="N28528">Septimò, diceret aliquis velocitatem C decurſo CD, eſſe ſubduplam
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              velocitatis B decurſo BF; </s>
              <s id="N2852E">ſed velocitas C, decurſo CG, eſt dupla velo­
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              citatis eiuſdem C decurſo CD; </s>
              <s id="N28534">igitur velocitas C, decurſo CG, eſt
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              æqualis velocitati B, decurſo BF; igitur æqualis ictus. </s>
              <s id="N2853A">Reſp. conceſſa
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              primâ conſequentiâ, vltimâ verò negatâ; </s>
              <s id="N28540">quia non tantùm impetus
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              puncti C incutit ictum ſed totius CA, qui cenſetur eſſe collectus in
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              malleo in quo eſt quaſi centrum huius impetus, vt iam explicuimus
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              aliàs; ſed velocitas totius CA confecto CAD eſt æqualis velocitati
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              totius BA confecto BAF, cuius velocitas CA confecto CAG eſt dupla,
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              vt iam probatum eſt. </s>
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            <p id="N2854E" type="main">
              <s id="N28550">Octauò, hinc ictus CA confecto CAD eſt æqualis ictui AB con­
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              fecto BAF, & ictus CA confecto CI duplo CD eſt ad ictum CA con­
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              fecto CD, vt radix CA ad radicem CI: </s>
              <s id="N28558">hinc vides hunc motum con­
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              uenire in eo cum recto, quòd ſcilicet ictus inflictus motu recto à mi­
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              nori mole, ſit ad ictum maioris, ſuppoſita linea motus æquali in ratio­
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              ne ſubduplicata ponderum; quòd dicitur etiam de motu circulari duo­
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              rum fuſtium inæqualium, quorum ictus ſunt in ratione ſubduplicata
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              longitudinum, aſſumptis duntaxat arcubus æqualibus ab extremitate
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              vtriuſque decurſis. </s>
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            <p id="N28568" type="main">
              <s id="N2856A">Nonò, cum mallei ſunt diuerſi ponderis, & longitudinis, facilè co­
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              gnoſci poterit proportio ictuum; </s>
              <s id="N28570">eſt enim compoſita ex ratione lon­
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              gitudinum & ſubduplicata ponderum v.g. ſit malleus A, cuius longitu­
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              do ſit 2. pondus 4. ſit malleus B cuius longitudo ſit pondus; </s>
              <s id="N2857A">rectè ra­
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              tio longitudinum eſt 2/3, & ſubduplicata ponderum eſt 2/3; </s>
              <s id="N28580">ducatur vna
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              in aliam, vt euadat compoſita ſcilicet 4/1 vel longitudo A ſit I, & B 2; </s>
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              habebitur ratio ſubduplicata ponderum 2/1, & ratio longitudinum 3/2; </s>
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              ducatur vna in aliam, habebitur ratio compoſita 2/2; </s>
              <s id="N28594">igitur ſunt æqua-</s>
            </p>
          </chap>
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    </archimedes>
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