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Page 02 Isaac Newton

        thefe Matters,  I baoe bitber to de-Layed the printing,  and fbould ftill baoe delayed it,  bad not the Importunity of friends prevailed upon me If any other Papers writ on this Subject are got out of my Hands they are imperfect, and were perbaps written before I bad tried all the Experiments bere fet down,  and fully fatisfi-ed my felf about the laws of Re-fractions and Competition of Co-lours. 






       I baoe bere Publifb'd what I tbink proper to come abroad,  wifbing that it may not be translated into another Language with- out my Content.



     The Crowns of Colours. which fo me times appear about the Sun and Moon, I baoe endeavoured to gioc an Account of,  but for 

          Want......!! 

       

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   want of fufficient Obferoations leaue that Matter to be Farther examined. 

   

    The Subject of the Tbird Book I baoe alfo left im- perfect,  not bauing tried all the Experiments which I intended when I was about thefe Matters,  nor repeated fome of tbofe which I did try,

    

     until I bad fatisfied my felf about all tbeir Circum- ftances. To communicate what I have tried, and leave the reft to other for fathers Enquiry, is all my Defign in publifbing thefe Papers. 


    In a Letter written to Mr. Lied-nitz in the Tear 1679, and put- lifbed by Dr. Wallis, I mention'd a Mitbod by which I bad Found fome general Theorems about Jquaring Curvilinear Figures, 

                                Or 



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        or comparing them with the Co-nic Sections,  or other the Jumplejt Figures with which they may be compared.  Any tome Tears ago I lent aut a Mannjcript contain-ing Jucb Tbeorems,  and baving fince met with fome Things copied out of it, I bave on this Occafion made it publick,  prefixing to it an Introduction, and fubjioning a Scholium concerning that Matbad.

     

      And I bave joined with it another famll Tract concerning the Curvilinear Figures of the Second Kind,  which was alfo written many Tears ago. And made known to fome Friends, who have folicited the making it publick.

      April r. 

      1704.                                 I. N 

      

   

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 [ 5 ] A X. I. T B E Angles of Reflexion, and Refraction, lie one and additionally the celebrity Plane with the Angle of Incidence. A X. II. The Angle of Reflexion is up to the Angle of Incidence. A X. III. If the Refracted Ray be came back directly back to the aim of Incidence, it fball be re-fracted into the road before defcribed by the in-cident Ray. A X. IV. Refraction out of the rarer Medium into the denfer, is made towards the Perpendicular, that is, of that the Angle of Refraction be lefs than the Angle of Incidence. A X. V. The mathematical function of Incidence is eitber accurately or really nearly terribly} very given relation to the mathematical function of Re-fraction. wherefrom if that Proportion be acknowledged in anybody Inclination of the incident Ray, 'tis acknowledged in all the Inclinations, and thereby the Refra-ction in all cafes of Incidence on the celebrity refra-cting Body may even be determined. therefore if the Refra-