https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/ {Braces} are inserted by the Transcriber to clarify the meaning of maths expressions. Overlining is the method of grouping used in the original and is marked [=like this]. In Lib. I. Lemma XVIII. & XX. [r] is upright r distinguished from italics, in Lemma XVIII. [s] is long-s... la https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/6/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/6/ Casus ubi dantur tria puncta sic solvitur expeditius. Dentur puncta B, C, D. Junctas BC, CD produc ad E, F, ut sit EB ad EC ut SB ad SC, & FC ad FD ut SC ad SD. Ad EF ductam & p... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/10/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/10/ Problema solvitur Arithmetice faciendo ut orbis, quem corpus in Ellipsi mobili, ut in Propositionis superioris Corol. 2. vel 3. revolvens, describit in plano immobili, accedat a... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/18/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/18/ _Corol. 1._ Hinc si AB æquetur quartæ parti ipsius AC, spatium ABRP, quod corpus tempore quovis ATD cadendo describit, erit ad spatium quod corpus semisse velocitatis maximæ AC,... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/30/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/30/ Diximus aream, quam Luna radio ad Terram ducto describit, esse tempori proportionalem, nisi quatenus motus Lunaris ab actione Solis turbatur. Inæqualitatem momenti (vel incremen... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/5/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/5/ Sunto CA, CB semi-axes Hyperbolæ; PG, KD diametri conjugatæ; PF, Qt perpendicula ad diametros; & Qv ordinatim applicata ad diametrum GP. Agatur SP secans tum diametrum DK in E,... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/8/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/8/ Intra Ovalem detur punctum quodvis, circa quod ceu polum revolvatur perpetuo linea recta, & interea in recta illa exeat punctum mobile de polo, pergatq; semper ea cum velocitate... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/9/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/9/ De loco quovis A in recta ADEC cadat corpus E, deq; loco ejus E erigatur semper perpendicularis EG, vi centripetæ in loco illo ad centrum C tendenti proportionalis: Sitq; BFG li... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/19/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/19/ Centro C, Asymptotis rectangulis CADd & CH describatur Hyperbola BEeS, & Asymptoto CH parallelæ sint AB, DE, de. In Asymptoto CD dentur puncta A, G: Et si tempus exponatur per a... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/7/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/7/ Igitur si figura rectilinea in aliam transmutanda est, sufficit rectarum intersectiones transferre, & per easdem in figura nova lineas rectas ducere. Sin curvilineam transmutare... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/31/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/31/ _Corol._ Igitur cum, in data Nodorum positione, summa omnium arearum pDdm, quo tempore Luna pergit à Quadratura ad locum quemvis m, sit area mpQEd, quæ ad Ellipseos Tangentem QE... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/15/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/15/ _Exempl. 3._ Si Vis centripeta, ad singulas Sphæræ particulas tendens, decrescit in quadruplicata ratione distantiæ a particulis, scribe PE^4 ÷ 2AS^3 pro V, dein [sqrt]2PS × LD... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/14/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/14/ Sint AHKB, ahkb æquales duæ superficies Sphæricæ, centris S, s, diametris AB, ab descriptæ, & P, p corpuscula sita extrinsecus in diametris illis productis. Agantur a corpusculi... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/21/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/21/ _Corol. 6._ Sed & in Medio non resistente quantitas Materiæ pendulæ est ut pondus comparativum & quadratum temporis directe & longitudo penduli inverse. Nam pondus comparativum... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/4/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/4/ Quæ de curvis lineis deq; superficiebus comprehensis demonstrata sunt, facile applicantur ad solidorum superficies curvas & contenta. Præmisi vero hæc Lemmata ut effugerem tædiu... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/24/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/24/ In Tabula priore seligendo ex observationibus tertiam, quintam & septimam, & exponendo velocitates maximas in his observationibus particulatim per numeros 1, 4, 16 respective, &... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/17/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/17/ _Corol. 1._ Hinc si vertice D, Diametro DE deorsum producta, & latere recto quod sit ad 2DP ut resistentia tota, ipso motus initio, ad vim gravitatis, Parabola construatur: velo... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/16/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/16/ Si corpus aliquod perpendiculariter versus planum datum trahatur, & ex data lege attractionis quæratur motus corporis: Solvetur Problema quærendo (per Prop. XXVII.) motum corpor... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/33/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/33/ Confirmatur etiam propinquitas Cometarum ex luce capitum. Nam corporis coelestis à Sole illustrati & in regiones longinquas abeuntis diminuitur splendor in quadruplicata ratione... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/28/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/28/ _Corol. 2._ Igitur corpora universa quæ circa Terram sunt, gravia sunt in Terram; & pondera omnium, quæ æqualiter à centro Terræ distant, sunt ut quantitates materiæ in iisdem.... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/11/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/11/ Centro quovis G, intervallo GH Cycloidis arcum RS æquante, describe semicirculum HKMG semidiametro GK bisectum. Et si vis centripeta distantiis locorum a centro proportionalis t... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/20/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/20/ _Cas. 2._ Dico jam quod fluidi hujus partes omnes sphæricæ æqualiter premuntur undique: sit enim EF pars sphærica fluidi, & si hæc undiq; non premitur æqualiter, augeatur pressi... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/12/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/12/ Corpora, per Theorema novissimum, perinde movebuntur, ac si a corpore tertio in communi gravitatis centro constituto traherentur; & centrum illud ipso motus initio quiescet (per... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/34/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/34/ | Tem. |Temp. | | | Lat. | | appar. |ver[=u] | Long. Solis | Long. Cometæ | Cometæ | +--------+---------+---------------+--------------+---------+ 1680 12| 4.46 | 4.46.00 |[Cap.... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/3/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/3/ Hactenus principia tradidi a Mathematicis recepta & experientia multiplici confirmata. Per leges duas primas & Corollaria duo prima adinvenit _Galilæus_ descensum gravium esse i... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/22/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/22/ _Corol. 1._ Hinc si corpora duo quævis, quæ similia sint & ad Systematum particulas correspondentes similiter sita, inter ipsas temporibus proportionalibus similiter moveri inci... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/13/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/13/ _Corol. 10._ Ut rationem ineamus errorum in latitudinem, fingamus planum Orbis QES immobile manere; & ex errorum exposita causa manifestum est, quod ex viribus NM, ML, quæ sunt... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/1/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/1/ {Braces} are inserted by the Transcriber to clarify the meaning of maths expressions. Overlining is the method of grouping used in the original and is marked [=like this]. In Li... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/27/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/27/ Proprietates autem Vorticum hac Propositione investigare conatus sum, ut pertentarem siqua ratione Phænomena coelestia per Vortices explicari possint. Nam Phænomenon est quod Pl... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/32/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/32/ Vis Lunæ ad mare movendum colligenda est ex ejus proportione ad vim Solis, & hæc proportio colligenda est ex proportione motuum maris, qui ab his viribus oriuntur. Ante ostium f... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/23/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/23/ Denique si aqua per canalem horizonti parallelum egrediatur; quoniam fundum vasis integrum est, & eadem aquæ incumbentis pressione ubique urgetur ac si aqua non efflueret; vas s... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/35/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/35/ Caudas autem à capitibus oriri & in regiones à Sole aversas ascendere confirmatur ex legibus quas observant. Ut quod in planis orbium Cometarum per Solem transeuntibus jacentes,... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/26/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/26/ Spectant Propositiones novissimæ ad motum Lucis & Sonorum. Lux enim cum propagetur secundum lineas rectas, in actione sola (per Prop. XLI. & XLII.) consistere nequit. Soni vero... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/25/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/25/ _Cas. 2._ Ponamus jam quod de, fg, hi, kl, mn designent pulsus a puncto A per Medium Elasticum successive propagatos. Pulsus propagari concipe per successivas condensationes & r... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/29/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/29/ Quoniam pondera inæqualium crurum canalis aqueæ ACQqca æqualia sunt; & pondera partium, cruribus totis proportionalium & similiter in totis sitarum, sunt ad invicem ut pondera t... https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/2/ https://www.cyberlibrary.org/la/books/philosophiae-naturalis-principia-mathematica-28233/chapters/2/ Effectus quibus motus absoluti et relativi distinguuntur ab invicem, sunt vires recedendi ab axe motus circularis. Nam in motu circulari nude relativo hæ vires nullæ sunt, in ve...