Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              primum, ſed non ſunt æqualia, vt conſtat; </s>
              <s id="N17D04">alioquin duobus illis inſtanti
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              bus motus eſſet æquabilis; igitur ſecundum eſt maius tertio, ita vt tamen
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              ex vtroque tempus fiat æquale primo inſtanti. </s>
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            <p id="N17D0C" type="main">
              <s id="N17D0E">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              64.
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              </s>
            </p>
            <p id="N17D1A" type="main">
              <s id="N17D1C">
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              Non decreſcunt illa inſtantia ſecundum lineam ſextam in extremam &
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              mediam rationem propagatam; </s>
              <s id="N17D24">ita vt primum ſit ad ſecundum, vt ſecundum
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              ad tertium, tertium ad quartum, quartum ad quintum at que ita deinceps
                <emph.end type="italics"/>
              ; </s>
              <s id="N17D2D">
                <lb/>
              ſit enim aliqua ſeries numerorum, qui aliquo modo accedant ad prædi­
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              ctam proportionem 1.2.3.5.8.13.21.34.55. ſitque primum inſtans vlti­
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              mus numerus 55. ſecundum 34.tertium 21. atque ita deinceps: </s>
              <s id="N17D36">Equidem
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              ſecundum, & tertium adæquant primum; </s>
              <s id="N17D3C">at verò quartum, quintum,
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              ſextum nullo modo adæquant; </s>
              <s id="N17D42">immò ne quidem eius ſubduplum, &
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              multò minus 3. alij addito primo: </s>
              <s id="N17D48">immò ſi linea data duodecies propor­
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              tionaliter diuidatur, vltimum ſegmentum vix eſſet ſubcentuplum primi,
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              vt conſtat; igitur reiici debet hæc propoſitio. </s>
            </p>
            <p id="N17D50" type="main">
              <s id="N17D52">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              65.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N17D5E" type="main">
              <s id="N17D60">
                <emph type="italics"/>
              Inſtans primum non eſt ad ſecundum vt numerus ad numerum; </s>
              <s id="N17D66">nec ad
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              tertium, quartum, quintum, ſextum, &c.
                <emph.end type="italics"/>
              probatur, quia nullus numerus
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              excogitari poteſt quo deſignari poſſit quantitas, ſeu perfectio, ſeu va­
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              lor iſtorum inſtantium; </s>
              <s id="N17D73">ſit enim primum inſtans ſecundum ſit 3/5. tertium
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              2/5 quartum 4/9 quintum 2/9 ſextum 2/9. Equidem ſecundum, & tertium adę­
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              quant primum; </s>
              <s id="N17D7D">adde quod non poteſt amplius ſeries propagari per nu­
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              meros rationales; </s>
              <s id="N17D83">ſit autem ſecundum (6/11) 3. (5/11) cum tribus aliis 4/9 1/9 7/9; </s>
              <s id="N17D87">
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              equidem ſi reducantur hæ 5. minutiæ, reſpondebunt his (54/99) (45/99) (44/99) (12/99) (26/99): </s>
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              igitur ſecunda erit maior quarta; </s>
              <s id="N17D91">at prima ſuperat ſecundam (9/999) ſecunda
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              tertiam (1/99) tertia quartam (11/99) quarta quintam (12/99). Cur porrò hæc inæqua­
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              litas, igitur numeri poſſunt aſſignari; non poſſunt etiam poni in ſerie
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              geometrica ſubdupla 1. 1/2 1/4 1/8 &c. </s>
              <s id="N17D9B">quia ſecunda. </s>
              <s id="N17D9E">& tertia non adæquant
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              primam idem dicendum eſt potiori iure de tribus aliis; </s>
              <s id="N17DA4">nec etiam in ſe­
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              rie arithmetica ſimplici 1. 1/2 1/3 1/4 2/5 1/6; quia ſecunda, & tertia ſunt mi­
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              nores prima 1/6, vt quarta, quinta, ſexta ſunt minores prima (26/74). </s>
            </p>
            <p id="N17DAC" type="main">
              <s id="N17DAE">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              66.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N17DBA" type="main">
              <s id="N17DBC">
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              Datur aliquis ſeries numerorum irrationabilium, ſeu ſurdorum minorum, &
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              minorum
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              ; quorum primus ita ſuperet ſecundum, ſecundus tertium,
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              tertius quartum, &c. </s>
              <s id="N17DC9">vt ſecundus, & tertius adæquent primum, item
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              quartus, quintus, ſextus. </s>
              <s id="N17DCE">item 4. alij, qui ſequuntur, item 5. item 6. &c. </s>
              <s id="N17DD1">
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              v. g. poteſt dari linea AG conſtans tribus partibus æqualibus, ſcilicet
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              AB, BC, CG, & ſecunda BC duabus BD maiore, & DC minore, & ter­
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              tia tribus prima CE minore ED, ſed maiore EF, ſecunda EF maiore F
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              G, atque ita deinceps; </s>
              <s id="N17DE0">addi poteſt quartum ſegmentum æquale AB; </s>
              <s id="N17DE4">quod
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              ſubdiuidetur in 4. partes, quarum prima ſit maior ſecunda, &
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              tertia
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              & hæc quarta, & omnes minores FG; </s>
              <s id="N17DF0">ita autem ſuperant primæ ſequen­
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              tes, vt differentia primæ, & ſecundæ ſit maior differentia ſecundæ, & </s>
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          </chap>
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