Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Concipe igitur punctum
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G
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motu continuo percurrere puncta om
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nia figuræ primæ, & punctum
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g
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motu itidem continuo percurret
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puncta omnia figuræ novæ & eandem deſcribet. </
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<
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tia nominemus
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DG
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ordinatam primam,
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dg
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ordinatam novam;
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AD
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abſciſſam primam,
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ad
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abſciſſam novam;
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O
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polum,
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OD
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ra
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dium abſcidentem,
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OA
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radium ordinatum primum, &
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Oa
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(qno
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parallelogrammum
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OABa
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completur) radium ordinatum novum. </
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DE MOTU
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CORPORUM</
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G
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tangit rectam Lineam poſitione da
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tam, punctum
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g
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tanget etiam Lineam rectam poſitione datam. </
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<
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punctum
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G
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tangit Conicam ſectionem, punctum
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g
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tanget etiam
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Conicam ſectionem. </
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Porro ſi punctum
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G
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tan
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git Lineam tertii ordinis
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Analytici, punctum
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g
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tanget Lineam tertii iti
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dem ordinis; & ſic de
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curvis lineis ſuperiorum
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ordinum. </
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<
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>Lineæ duæ e
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runt ejuſdem ſemper or
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dinis Analytici quas pun
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cta
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G, g
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tangunt. </
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<
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enim ut eſt
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ad
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ad
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OA
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ita ſunt
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Od
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ad
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OD, dg
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ad
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DG,
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&
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AB
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ad
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AD
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; adeoque
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AD
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æqualis eſt (
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OAXAB/ad
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), &
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DG
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æqualis eſt (
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OAXdg/ad
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). Jam ſi punc
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tum
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G
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tangit rectam Lineam, atque adeo in æquatione quavis,
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qua relatio inter abſciſſam
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AD
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& ordinatam
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DG
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habetur, in
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determinatæ illæ
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AD
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&
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DG
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ad unicam tantum dimenſionem
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aſcendunt, ſcribendo in hac æquatione (
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OAXAB/ad
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) pro
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AD,
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&
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(
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OAXdg/ad
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) pro
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DG,
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producetur æquatio nova, in qua abſciſſa no
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va
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ad
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& ordinata nova
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dg
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ad unicam tantum dimenſionem aſcen
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dent, atque adeo quæ deſignat Lineam rectam. </
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<
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AD
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&
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DG
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(vel earum alterutra) aſcendebant ad duas dimenſiones in æquati
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one prima, aſcendent itidem
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ad
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&
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dg
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ad duas in æquatione ſecun
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da. </
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<
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<
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ad, dg
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in æquatione ſecunda &
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AD, DG
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in prima aſcendent ſem
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per ad eundem dimenſionum numerum, & propterea Lineæ, quas
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puncta
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G, g
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tangunt, ſunt ejuſdem ordinis Analytici. </
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