Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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ſcilicet toto niſu applicata, ſit etiam longitudo AC dupla AB: </
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<
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quod eodem tempore H acquiret æquale ſpatium ſcilicet CAD; </
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<
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N284CF
">igitur
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CAD eſt 1/4 CAG, quia eſt æquale BAF; </
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<
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N284D5
">igitur CD eſt 1/4 CG, ſed
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CG eſt duplus BF; </
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<
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">igitur CD eſt ſubduplus BF; </
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<
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">igitur velocitas ex
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tremitatis C in CA eſt ſubdupla velocitatis B in BA: </
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<
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">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. </
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<
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">Sextò, ictus inflicti à malleis, quorum manubria diuerſam longitu
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dinem habent, ſuppoſito eodem angulo, ſunt vt longitudines; </
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<
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">ſi enim
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eo tempore, quo AB facit ſpatium BAF, AC facit CAD; </
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<
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">certè æquali
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tempore AC faciet DAG, vt conſtat ex natura motus accelerati; </
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igitur acquirit
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impetus; </
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">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; </
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<
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">igitur AC decurſo CAG habet duplum impetum AB decurſo
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BAF; </
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<
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id
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N2851C
">igitur dupla eſt vis ictus; </
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<
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id
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">igitur ictus ſunt in ratione ſubdupli
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cata CAG, BAF; igitur vt ACAB. </
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<
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">Septimò, diceret aliquis velocitatem C decurſo CD, eſſe ſubduplam
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velocitatis B decurſo BF; </
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<
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id
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">ſed velocitas C, decurſo CG, eſt dupla velo
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citatis eiuſdem C decurſo CD; </
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<
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id
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">igitur velocitas C, decurſo CG, eſt
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æqualis velocitati B, decurſo BF; igitur æqualis ictus. </
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<
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">Reſp. conceſſa
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primâ conſequentiâ, vltimâ verò negatâ; </
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<
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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. </
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<
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">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: </
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<
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">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. </
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<
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id
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">Nonò, cum mallei ſunt diuerſi ponderis, & longitudinis, facilè co
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gnoſci poterit proportio ictuum; </
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<
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id
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">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; </
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<
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">rectè ra
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tio longitudinum eſt 2/3, & ſubduplicata ponderum eſt 2/3; </
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<
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">ducatur vna
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in aliam, vt euadat compoſita ſcilicet 4/1 vel longitudo A ſit I, & B 2; </
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habebitur ratio ſubduplicata ponderum 2/1, & ratio longitudinum 3/2; </
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ducatur vna in aliam, habebitur ratio compoſita 2/2; </
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<
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