Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of contents

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[101.] Addenda Lectionibus Geometricis.
Page: 342 (149)
[102.] _Probl_. I.
Page: 342 (149)
[103.] _Probl_. II.
Page: 342 (149)
[104.] _Probl_. III.
Page: 342 (149)
[105.] Addenda Lectionibus Geometricis.
Page: 343 (150)
[106.] _Theor_. I.
Page: 343 (150)
[107.] _Theor_. II.
Page: 343 (150)
[108.] _Theor_. III.
Page: 343 (150)
[109.] _Theor_. IV.
Page: 344 (151)
[110.] _Theor_. V.
Page: 344 (151)
[111.] _Theor_. VI.
Page: 344 (151)
[112.] FINIS.
Page: 344 (151)
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          <p>
            <s xml:id="echoid-s8795" xml:space="preserve">
              <pb o="21" file="0199" n="214" rhead=""/>
            unius anguli rectilinei circa alterum _Conica Superficies_; </s>
            <s xml:id="echoid-s8796" xml:space="preserve">ex rectanguli
              <lb/>
            trianguli circa crus unum anguli recti _conus_ ipſe deſormatur; </s>
            <s xml:id="echoid-s8797" xml:space="preserve">eóque
              <lb/>
            pacto _cùm integræ cum ſuis Curvis Superficiebus Solidæ magnitudines_
              <lb/>
            _innumeræ, tumipſarum portiones, fruſta, tubi, annuli procreantur._
              <lb/>
            </s>
            <s xml:id="echoid-s8798" xml:space="preserve">Cujuſmodi motûs hæc præcipua proprietas eſt, quòd ſingula quæque
              <lb/>
            magnitudinis circumductæ puncta peripherias obeant circulares (inte-
              <lb/>
            gras quidem illas, modò perfecta ſit revolutio, ſeu mobile denuo
              <lb/>
            primum in ſitum reſtituatur, at ſimiles utcunque ſibi mutuo, quæ
              <lb/>
            ſimul deſcribuntur) quarum omnia Centra ſunt in dicto axe, radii
              <lb/>
            verò ſunt rectæ ab ipſis punctis ad axem perpendiculares. </s>
            <s xml:id="echoid-s8799" xml:space="preserve">Vel; </s>
            <s xml:id="echoid-s8800" xml:space="preserve">
              <lb/>
            quod omnes in mobili ſitæ rectæ lineæ axi perpendiculares eſſiciunt
              <lb/>
            circulos (ſi revolutio ponatur integrè peracta) aut circulares ſimiles
              <lb/>
            ſectores, illos intelligo qui ſimul eodem tempore delineantur. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">Ut ſi
              <lb/>
              <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">Fig. 9.</note>
            v.</s>
            <s xml:id="echoid-s8802" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8803" xml:space="preserve">linea quævis circa axem VK rotetur, eo procreabitur motu curva
              <lb/>
            quædam Superficies, circularibus quaſi peripheriis conſtans (_Ato-_
              <lb/>
            _miſtarum_ enim phraſin facilitatis, perſpicuitatis, brevitatis, addere
              <lb/>
            licet & </s>
            <s xml:id="echoid-s8804" xml:space="preserve">veriſimilitudinis causâ non illibenter uſurpo) circularibus, in-
              <lb/>
            quam, peripheriis AY, BY, CY, DY per puncta A, B, C, D reli-
              <lb/>
            quáque quæ ſunt in VD cuncta decircinatis; </s>
            <s xml:id="echoid-s8805" xml:space="preserve">quarum radii ſunt rectæ
              <lb/>
            AZ, BZ, CZ, DZ axi perpendiculares, & </s>
            <s xml:id="echoid-s8806" xml:space="preserve">Centra Z in axe.
              <lb/>
            </s>
            <s xml:id="echoid-s8807" xml:space="preserve">Quód ſi revolutio tantum eouſque continuatur, donec VAD ſit in
              <lb/>
            ſitu V αδ, conſtabit _effecta superficies_ ex arcubus A α, B ε
              <unsure/>
            , C γ,
              <lb/>
            D δ, ſimilibus inter ſe eodem modo ſi planum VDZ circa axem
              <lb/>
            VK revolvatur, poſito quòd integra peragatur converſio, produ-
              <lb/>
            cetur Solidum quali conſtans innumeris circulis parallelis AY, BY,
              <lb/>
            CY, DY, quorum (ut priùs) radii AZ, BZ, CZ, DZ,
              <lb/>
            centra Z; </s>
            <s xml:id="echoid-s8808" xml:space="preserve">poſitóque quod circulatio deſiſtit in ſitu δ υ K, conſtitue-
              <lb/>
            tur Solidum è Sectoribus AZ α, BZ ε
              <unsure/>
            , CZ γ, & </s>
            <s xml:id="echoid-s8809" xml:space="preserve">reliquis inter ſe
              <lb/>
            ſimilibus. </s>
            <s xml:id="echoid-s8810" xml:space="preserve">Cæterúm prætermittenda non eſt animadverſio quædam
              <lb/>
            perquam utilis, & </s>
            <s xml:id="echoid-s8811" xml:space="preserve">neceſſaria circa _modum Superficierum, & </s>
            <s xml:id="echoid-s8812" xml:space="preserve">Soli-_
              <lb/>
            _dorum hoc modo reſultantium dimenſiones inveſtigandi juxta metbodum_
              <lb/>
            _indiviſibilium, omnium expeditiſſimam, & </s>
            <s xml:id="echoid-s8813" xml:space="preserve">modò ritè adhibeatur haud_
              <lb/>
            _minùs certam & </s>
            <s xml:id="echoid-s8814" xml:space="preserve">infallibilem._ </s>
            <s xml:id="echoid-s8815" xml:space="preserve">Objicit huic methodo non ſemel, in
              <lb/>
            pererudito ſuo de _Solidis cylindricis ac annularibus libello, do
              <unsure/>
            ctiſſimus_
              <lb/>
            _A. </s>
            <s xml:id="echoid-s8816" xml:space="preserve">Tacquetus_, eóque ſe putat illam deſtruere, quòd per eam in-
              <lb/>
            ventæ _conorum, & </s>
            <s xml:id="echoid-s8817" xml:space="preserve">Spherarum ſuperſicies_ (quantitates horum intelligo)
              <lb/>
            veræ per _Archimedem_ repertæ ac traditæ dimenſioni non reſpondent. </s>
            <s xml:id="echoid-s8818" xml:space="preserve">
              <lb/>
            Sit exemplo _rectus conus_ DVY, cujus axis VK; </s>
            <s xml:id="echoid-s8819" xml:space="preserve">per cujus omnia
              <lb/>
            puncta tranſire concipiantur axi perpendiculares rectæ ZA, ZB,
              <lb/>
            ZC, | ZD, &</s>
            <s xml:id="echoid-s8820" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8821" xml:space="preserve">è quibus nempe juxta _methodum atomicam_ com-
              <lb/>
              <note position="right" xlink:label="note-0199-02" xlink:href="note-0199-02a" xml:space="preserve">Fig. 10, 11, 12.</note>
            | K
              <unsure/>
            </s>
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