Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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            <s xml:id="echoid-s4413" xml:space="preserve">
              <pb o="480" file="0200" n="210" rhead="JAC. GREG. CONSID."/>
            cujus poteſtatis puræ, ſive affectæ ad puram irreducibilis.
              <lb/>
            </s>
            <s xml:id="echoid-s4414" xml:space="preserve">Nam ſi Sector eodem modo fiat cx primis terminis conver-
              <lb/>
            gentibus, quo ex ſecundis (ut in Conſect. </s>
            <s xml:id="echoid-s4415" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s4416" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4417" xml:space="preserve">eſt de-
              <lb/>
            monſtratum) etiam omnes ejus poteſtates ſive puræ, ſive
              <lb/>
            quocunque modo affectæ eodem modo componitur è pri-
              <lb/>
            mis, quo è ſecundis terminis convergentibus, quæ (in A-
              <lb/>
            nalyticis exhibitæ) erunt æquales quantitates eodem modo
              <lb/>
            Analyticè compoſitæ ex primis, quo ex ſecundis terminis
              <lb/>
            convergentibus; </s>
            <s xml:id="echoid-s4418" xml:space="preserve">quod eſt abſurdum, nempe contra Prop. </s>
            <s xml:id="echoid-s4419" xml:space="preserve">
              <lb/>
            11. </s>
            <s xml:id="echoid-s4420" xml:space="preserve">admiſlam. </s>
            <s xml:id="echoid-s4421" xml:space="preserve">Senſus igitur integer Prop. </s>
            <s xml:id="echoid-s4422" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4423" xml:space="preserve">eſt Hoc Pro-
              <lb/>
            blema (E datis duobus polygonis complicatis, invenire Se-
              <lb/>
            ctorem ſive Circularem ſive Hyperbolicum ab illis determi-
              <lb/>
            natum) non poteſt reduci ad ullam æquationem Analyticam.</s>
            <s xml:id="echoid-s4424" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4425" xml:space="preserve">In comparatione Hugeniana inter noſtras methodos, a-
              <lb/>
            gnoſco, meas approximationes prop. </s>
            <s xml:id="echoid-s4426" xml:space="preserve">20. </s>
            <s xml:id="echoid-s4427" xml:space="preserve">& </s>
            <s xml:id="echoid-s4428" xml:space="preserve">21. </s>
            <s xml:id="echoid-s4429" xml:space="preserve">eaſdem eſſe
              <lb/>
            cum Hugenianis, ſed methodo mihi peculiari demonſtratas.
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            </s>
            <s xml:id="echoid-s4430" xml:space="preserve">At meam approximationem in fine prop. </s>
            <s xml:id="echoid-s4431" xml:space="preserve">25. </s>
            <s xml:id="echoid-s4432" xml:space="preserve">non percipere
              <lb/>
            videtur Hugenius; </s>
            <s xml:id="echoid-s4433" xml:space="preserve">aliam interim ſibi fingit: </s>
            <s xml:id="echoid-s4434" xml:space="preserve">hanc primò
              <lb/>
            meam non eſſe probat, deinde tamen eam cum ſua compa-
              <lb/>
            rat, victoriaque potitur. </s>
            <s xml:id="echoid-s4435" xml:space="preserve">Sed lentè hic feſtinandum.</s>
            <s xml:id="echoid-s4436" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4437" xml:space="preserve">Sit a Polygonum, Circulo vel ſectori inſcriptum, c Po-
              <lb/>
            lygonum inſcriptum duplo plura habens latera, d autem ſit
              <lb/>
            Polygonum circumſcriptum ſimile ipſi c. </s>
            <s xml:id="echoid-s4438" xml:space="preserve">Ex 20. </s>
            <s xml:id="echoid-s4439" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s4440" xml:space="preserve">Sector
              <lb/>
            eſt major quam {4c - a;</s>
            <s xml:id="echoid-s4441" xml:space="preserve">/3} & </s>
            <s xml:id="echoid-s4442" xml:space="preserve">ex 21. </s>
            <s xml:id="echoid-s4443" xml:space="preserve">Sector eſt minor quam
              <lb/>
            {2d + c/3}, inter quos terminos ſit maximus quatuor continuè
              <lb/>
            proportionalium {8d + 8c-a/15}, nempe noſtra approximatio@
              <lb/>
            quam rigidiſſimis Hugenii cenſuris ſubjicio. </s>
            <s xml:id="echoid-s4444" xml:space="preserve">Hallucinatur au-
              <lb/>
            tem Hugenius, quod Polygona a & </s>
            <s xml:id="echoid-s4445" xml:space="preserve">d ſimilia ſumeret, cum
              <lb/>
            debeant eſſe c & </s>
            <s xml:id="echoid-s4446" xml:space="preserve">d, quæ duplò plura habent latera. </s>
            <s xml:id="echoid-s4447" xml:space="preserve">Ne
              <lb/>
            autem dicat, factam eſſe à me correctionem, conſideret
              <lb/>
            hanc approximationem non ſolum verbis prop. </s>
            <s xml:id="echoid-s4448" xml:space="preserve">25. </s>
            <s xml:id="echoid-s4449" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s4450" xml:space="preserve">
              <lb/>
            praxi prop. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4452" xml:space="preserve">eſſe conſonam, ubi approximationem prop.
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            </s>
            <s xml:id="echoid-s4453" xml:space="preserve">21. </s>
            <s xml:id="echoid-s4454" xml:space="preserve">ex ultimis ſimilibus Polygonis conſtruo: </s>
            <s xml:id="echoid-s4455" xml:space="preserve">ridiculum enim
              <lb/>
            eſſet, illam è penultimis minus præciſam dare, cum </s>
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