Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

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              quo percurretur DE, percurretur pluſquam DN; </s>
              <s id="N23836">quippe DN eſt minùs
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              inclinatus, quàm DE: </s>
              <s id="N2383C">porrò recta NH eodem deinde tempore percur­
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              retur, ſiue ducatur initium motus AD per arcum DN, ſiue AD per re­
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              ctam DN, ſiue ab O per rectam ON; quia in N eſt æqualis velocitas
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              per Lemm. </s>
              <s id="N23846">11. igitur tempus, quo percurritur recta NH, facto initio
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              motus ex D per rectam, vel arcum DN, eſt ad tempus, quo percurritur
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              DN, vt 42466.ad DN, id eſt ad 390181. ſit enim vt ON ad 111347.
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              ita hæc ad OH 179995. detrahatur ON ex 111347.ſupereſt 42466.igi­
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              tur eo tempore, quo percurritur DE, percurritur pluſquam DN; </s>
              <s id="N23852">per­
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              curritur tamen minùs, quàm DL; </s>
              <s id="N23858">quia tempus, quo percurritur DL eſt
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              ad tempus quo percurritur LH facto initio motus in D, vt DL 51764.
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              ad 41422. igitur eo tempore, quo percurritur DE; percurritur minùs
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              quàm DL. </s>
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              <s id="N23864">Adde quod rectæ DE, DM, æquali tempore percurruntur; </s>
              <s id="N23868">ſed DM
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              breuiore tempore percurritur, quàm arcus DL, immò arcus DE citiùs
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              peragitur, quàm recta DE; </s>
              <s id="N23870">igitur citiùs quàm arcus DL; </s>
              <s id="N23874">ſi verò acci­
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              piatur arcus DR; </s>
              <s id="N2387A">certè tempus per arcum DE eſt paulò minus tempo­
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              re per arcum DR; quia tempus, quo percurritur DR eſt ad tempus, quo
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              percurretur RH, facto initio motus in D, vt 45444.ad 41705.ſed vtrum­
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              que tempus debet eſſe æquale, vt ſcilicet arcus in DH æquali tempore
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              cum arcu DE percurratur. </s>
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            <p id="N23886" type="main">
              <s id="N23888">Obſeruabis præterea, vt inueniatur arcus quadrantis DH, cuius tem­
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              pus ſit ſubduplum ipſius quadrantis, vel æquale tempori per arcum DE,
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              aſſumendum eſſe punctum in arcu DH, puta N; </s>
              <s id="N23890">per quod ſi ducatur
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              HNO, ſitque vt ON ad OV, ita OV ad OH, ipſa NV erit æqualis
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              ipſi ND; </s>
              <s id="N23898">quippè tempus per DN eſt ad tempus per ON, vt ipſa DN ad
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              ON; </s>
              <s id="N2389E">ſed tempus per ON eſt ad tempus per NH, vt ON ad NV; </s>
              <s id="N238A2">igi­
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              tur tempus per DN eſt ad tempus per NH, vt DN ad NV; </s>
              <s id="N238A8">igitur DN,
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              & NH facto initio motus à D fiunt tempore æquali; </s>
              <s id="N238AE">ſed vt tempus per
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              rectam DN ad tempus per rectam NH; </s>
              <s id="N238B4">ita tempus per duas DXN ad
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              tempus per duas NZH; </s>
              <s id="N238BA">ita tempus per 4. æquales inſcriptas arcui DN
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              ad tempus per 4.æquales inſcriptas arcui NZH, atque ita deinceps; igi­
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              tur ita tempus per arcum DN ad tempus per arcum NZH. </s>
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            <p id="N238C2" type="main">
              <s id="N238C4">Quomodo verò poſſit inueniri punctum N, viderint Geometræ; </s>
              <s id="N238C8">nec
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              enim phyſici eſt inſtituti; habetur autem ex analytica, ſi excipiatur ar­
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              cus DN. 24. gra. </s>
              <s id="N238D0">20′. </s>
              <s id="N238D3">circiter; ſitque HO ſecans anguli AHO grad.57.
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              10′. </s>
              <s id="N238D8">ſitque ON, ad OV vt OV ad OH, ipſa NV erit proximè æqualis
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              ipſi ND: igitur DN. & NH æqualibus temporibus percurrentur. </s>
              <s id="N238DE">Simili­
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              ter opera eiuſdem analyticæ habebitur arcus, qui peragitur in DZH eo
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              tempore, quo arcus DNF percurritur, poſſuntque hæc omnia in cano­
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              nes redigi. </s>
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              Theorema
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              10.
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              In diuerſis punctis arcus diuerſus impetus producitur.
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              <s id="N238FE"> Prob. </s>
              <s id="N23901">ſit enim
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              pendulum fune ex centro immobili A; </s>
              <s id="N23907">ſitque AO horizontalis, AD </s>
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