Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of contents

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[151.] Fournier in Hydrographia 1. 12. C. 35.
[152.] Didericus Rembrantz a Nierop in Animadverſionibus de inveniendis longitudinibus.
[153.] BREVIS INSTRUCTIO DE USU HOROLO-GIORUM AD INVENIENDAS LONGITUDINES. I.
[154.] II.
[155.] III.
[156.] IV.
[157.] V. Reducere horologia ad rectam dierum menſuram vel cogno-ſcere quanto citius vel tardius ſpatio 24 horarum movean-tur.
[158.] VI. Ope Horologiorum mari invenire longitudinem loci in quo verſaris.
[159.] VII. Mari invenire horam diei.
[160.] VIII. Quomodo ex obſervatione ortus & occaſus Solis & ex hora horologiorum longitudo mari inveniri queat.
[161.] IX.
[163.] XI.
[164.] XII.
[165.] FINIS.
[166.] EXCERPTA EX LITERIS DATIS LONDINI {13/23} JANUARII MDCLXV.
[167.] EXCERPTA EX LITERIS HAGÆ CO-MITUM, DIE XXVI. FEBRUAR MDCLXV. DATIS.
[168.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA.
[169.] DE HUGENIANA CENTRI OSCILLATIONIS DETERMINATIONE CONTROVERSIA. I. Obſervationes Abbatis Catelani in propoſitio-nem, quæ fundamentum eſt 4æ. partis tra-ctatus de Pendulis, Hugenii.
[170.] II. Domini Abbatis Catelani Examen Ma-thematicum Centri Oſcillationis.
[171.] MONITUM.
[172.] III. Excerpta ex literis Domini Hugenii, quibus re-ſpondet obſervationi Abbatis Catelani in 4am. pro-poſitionem Tractatus de centris Oſcillationis.
[173.] IV. Exceptio Abbatis Catelani ad reſponſionem Hugenii.
[174.] V. Objectio Abbatis Catelani contra motum Pendulorum in Cycloidibus.
[175.] VI. Reſponſio ad objectiones Hugenii adverſus me-thodum Abbatis Catelani de determinan-do Centro Oſcillationis.
[176.] VII. Excerpta ex litteris D. Bernoullii datis Baſileæ ad Autorem Diarii Pariſienſis, de Controverſia, inter Abbatem Catelanum & Hugenium, de Centro Oſcillationis.
[177.] VIII. Excerpta ex literis Dni. Hugenii ad Auctores Diarii Pariſienſis, datis Hagæ 8. Funii 1684. quæ continent ejus reſponſionem ad exceptio-nem Dni. Abbatis Catelani, de cen-tro Oſcillationis.
[178.] IX. Reſponſio Dni. Abbatis Catelani ad literas Dni. Bernoulli de Controverſia ſua cum Dno. Hu-genio de centro Oſcillationis .
[179.] X. Dn. Bernouillii narratio controverſiæ inter Dn. Hugenium & Abbatem Catelanum agitatæ de Centro Oſcillationis, quæ loco Anim-adverſionis eſſe poterit in Reſpon-ſionem Dn. Catelani. Excerpta ex Litteris Dn. Bernoullii Lipſiam miſſis.
[180.] XI. Litteræ Dni Marchionis de l’Hôpital ad Dum Huge-nium, in quibus contendit, ſeregulam hujus Au-ctoris de Centro oſcillationis penduli compoſiti demonſtrare per cauſam Phyſicam, & re-ſpondere ſimul Dno Bernoulli.
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            <s xml:id="echoid-s2173" xml:space="preserve">Hanc cycloidis dimenſionem primus invenit, via tamen
              <lb/>
              <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE</emph>
              .</note>
            longe alia, eximius geometra Chriſtophorus Wren Anglus,
              <lb/>
            eamque deinde eleganti demonſtratione confirmavit, quæ
              <lb/>
            edita eſt in libro de cycloide viri clariſſimi Ioannis Walliſij.
              <lb/>
            </s>
            <s xml:id="echoid-s2174" xml:space="preserve">De eadem vero linea, alia quoque multa extant pulcherrima
              <lb/>
            inventa noſtri temporis mathematicorum, quibus præcipuè
              <lb/>
            occaſionem præbuere problemata quædam à Blaſio Paſchalio
              <lb/>
            Gallo propoſita, qui in his ſtudiis præcellebat. </s>
            <s xml:id="echoid-s2175" xml:space="preserve">Is cum ſua,
              <lb/>
            tum aliorum inventa recenſens, primum omnium Merſennum
              <lb/>
            lineam hanc in rerum natura advertiſſe ait. </s>
            <s xml:id="echoid-s2176" xml:space="preserve">Primum Roberval-
              <lb/>
            lium tangentes ejus definiviſſe, ac plana & </s>
            <s xml:id="echoid-s2177" xml:space="preserve">ſolida dimenſum eſſe. </s>
            <s xml:id="echoid-s2178" xml:space="preserve">
              <lb/>
            Item centra gravitatis tum plani, tum partium ejus inveniſſe. </s>
            <s xml:id="echoid-s2179" xml:space="preserve">
              <lb/>
            Primum Wrennium curvæ cycloidis æqualem rectam dediſ-
              <lb/>
            ſe. </s>
            <s xml:id="echoid-s2180" xml:space="preserve">Me quoque primum reperiſſe dimenſionem abſolutam por-
              <lb/>
            tionis cycloidis, quæ rectâ, baſi parallelâ, abſcinditur per
              <lb/>
            punctum axis, quod quarta parte ejus à vertice abeſt. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">quæ
              <lb/>
            nimirum portio æquatur dimidio hexagono æquilatero, intra
              <lb/>
            circulum genitorem deſcripto. </s>
            <s xml:id="echoid-s2182" xml:space="preserve">Seipſum denique ſolidorum
              <lb/>
            ac ſemiſolidorum, tam circa baſin quàm circa axem, centra
              <lb/>
            gravitatis definiviſſe, itemque partium eorum. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">Lineæ etiam
              <lb/>
            ipſius (Sed hæc poſt acceptam à Wrennio dimenſionem)
              <lb/>
            centrum gravitatis inveniſſe, & </s>
            <s xml:id="echoid-s2184" xml:space="preserve">dimenſionem ſuperficierum
              <lb/>
            convexarum, quibus ſolida iſta eorumque partes comprehen-
              <lb/>
            duntur; </s>
            <s xml:id="echoid-s2185" xml:space="preserve">earumque ſuperficierum centra gravitatis. </s>
            <s xml:id="echoid-s2186" xml:space="preserve">Ac denique
              <lb/>
            dimenſionem curvarum cujuſvis cycloidis, tam protractæ quam
              <lb/>
            contractæ: </s>
            <s xml:id="echoid-s2187" xml:space="preserve">hoc eſt earum quæ deſcribuntur à puncto intra
              <lb/>
            vel extra circumferentiam circuli genitoris ſumpto. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Et ho-
              <lb/>
            rum quidem demonſtrationes à Paſchalio ſunt editæ. </s>
            <s xml:id="echoid-s2189" xml:space="preserve">A qui-
              <lb/>
            bus ſuas quoque, de eadem linea, ſubtiliſſimas meditationes
              <lb/>
            expoſuit Cl. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">Walliſius, atque eadem illa omnia ſuo Marte
              <lb/>
            ſe reperiſſe, ac problemata à Paſchalio propoſita ſolviſſe con-
              <lb/>
            tendit. </s>
            <s xml:id="echoid-s2191" xml:space="preserve">Quod idem & </s>
            <s xml:id="echoid-s2192" xml:space="preserve">doctiſſimus Lovera ſibi vindicat. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">Quan-
              <lb/>
            tum vero unicuique debeatur, ex ſcriptis eorum eruditi dijudi-
              <lb/>
            cent. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">Nos propterea tantum præcedentia retulimus, quod ſi-
              <lb/>
            lentio prætereunda non videbantur egregia adeo inventa, qui-
              <lb/>
            bus factum eſt, ut, ex lineis omnibus, nulla nunc melius </s>
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