Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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unius anguli rectilinei circa alterum _Conica Superficies_; </
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<
s
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echoid-s8796
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xml:space
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">ex rectanguli
<
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trianguli circa crus unum anguli recti _conus_ ipſe deſormatur; </
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<
s
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echoid-s8797
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xml:space
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">eóque
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pacto _cùm integræ cum ſuis Curvis Superficiebus Solidæ magnitudines_
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_innumeræ, tumipſarum portiones, fruſta, tubi, annuli procreantur._
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</
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<
s
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xml:space
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">Cujuſmodi motûs hæc præcipua proprietas eſt, quòd ſingula quæque
<
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magnitudinis circumductæ puncta peripherias obeant circulares (inte-
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gras quidem illas, modò perfecta ſit revolutio, ſeu mobile denuo
<
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primum in ſitum reſtituatur, at ſimiles utcunque ſibi mutuo, quæ
<
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ſimul deſcribuntur) quarum omnia Centra ſunt in dicto axe, radii
<
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verò ſunt rectæ ab ipſis punctis ad axem perpendiculares. </
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<
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">Vel; </
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quod omnes in mobili ſitæ rectæ lineæ axi perpendiculares eſſiciunt
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circulos (ſi revolutio ponatur integrè peracta) aut circulares ſimiles
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ſectores, illos intelligo qui ſimul eodem tempore delineantur. </
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<
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echoid-s8801
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xml:space
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">Ut ſi
<
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">Fig. 9.</
note
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v.</
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<
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">g. </
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<
s
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echoid-s8803
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xml:space
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">linea quævis circa axem VK rotetur, eo procreabitur motu curva
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quædam Superficies, circularibus quaſi peripheriis conſtans (_Ato-_
<
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_miſtarum_ enim phraſin facilitatis, perſpicuitatis, brevitatis, addere
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licet & </
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<
s
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">veriſimilitudinis causâ non illibenter uſurpo) circularibus, in-
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quam, peripheriis AY, BY, CY, DY per puncta A, B, C, D reli-
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quáque quæ ſunt in VD cuncta decircinatis; </
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<
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xml:space
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">quarum radii ſunt rectæ
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AZ, BZ, CZ, DZ axi perpendiculares, & </
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<
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">Centra Z in axe.
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</
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<
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xml:space
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">Quód ſi revolutio tantum eouſque continuatur, donec VAD ſit in
<
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ſitu V αδ, conſtabit _effecta superficies_ ex arcubus A α, B ε
<
unsure
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, C γ,
<
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D δ, ſimilibus inter ſe eodem modo ſi planum VDZ circa axem
<
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VK revolvatur, poſito quòd integra peragatur converſio, produ-
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cetur Solidum quali conſtans innumeris circulis parallelis AY, BY,
<
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CY, DY, quorum (ut priùs) radii AZ, BZ, CZ, DZ,
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centra Z; </
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<
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">poſitóque quod circulatio deſiſtit in ſitu δ υ K, conſtitue-
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tur Solidum è Sectoribus AZ α, BZ ε
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, CZ γ, & </
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<
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">reliquis inter ſe
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ſimilibus. </
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<
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xml:space
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">Cæterúm prætermittenda non eſt animadverſio quædam
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perquam utilis, & </
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<
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">neceſſaria circa _modum Superficierum, & </
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<
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">Soli-_
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_dorum hoc modo reſultantium dimenſiones inveſtigandi juxta metbodum_
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_indiviſibilium, omnium expeditiſſimam, & </
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<
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">modò ritè adhibeatur haud_
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_minùs certam & </
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<
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">infallibilem._ </
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<
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xml:space
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">Objicit huic methodo non ſemel, in
<
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pererudito ſuo de _Solidis cylindricis ac annularibus libello, do
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ctiſſimus_
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_A. </
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<
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">Tacquetus_, eóque ſe putat illam deſtruere, quòd per eam in-
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ventæ _conorum, & </
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<
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">Spherarum ſuperſicies_ (quantitates horum intelligo)
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veræ per _Archimedem_ repertæ ac traditæ dimenſioni non reſpondent. </
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<
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Sit exemplo _rectus conus_ DVY, cujus axis VK; </
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<
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">per cujus omnia
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puncta tranſire concipiantur axi perpendiculares rectæ ZA, ZB,
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ZC, | ZD, &</
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<
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">c. </
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<
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">è quibus nempe juxta _methodum atomicam_ com-
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xlink:label
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note-0199-02
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">Fig. 10, 11, 12.</
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| K
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