The First Part Containing Book One,



Concerning the Explanation of the Principles, from which the Construction both of Telescopes as well as Microscopes is Desired.

     This is one of Euler's major works, extending over most of his working life; the chapters in the three volumes were produced mainly from his shorter articles produced over many years, and assembled with the help of his co-workers. At present,  volumes one and two are now completed.

chapter I  : Concerning the spreading of the image shown by a single lens.

chapter 2  : The spreading of the image presented by several lenses.

            chapter 3  : Concerning multiple or composite lenses.

            chapter 4  : Concerning the confusion of vision both by the apparent magnitude and clarity of the image.

            chapter 5  : Concerning the apparent field of view, with the eye at the most suitable place.

            chapter 6  : Concerning the confusion arising from the nature of diverse rays.

            chapter 7  : Concerning the construction of dioptric instruments in general.

             It is in this chapter in particular that Euler advocated the removal of the colored fringes round the image of an object viewed through a combination of lenses, by careful adjustments of the stops or diaphragms used : this assertion detracted considerably from the value of the work, as it was of course complete nonsense.

E266 achromatic doublet  : Construction of objective lenses from two glasses…..

The Second Part Containing Book Two :


            chapter 1  : Telescopes in general.

            chapter 2  : Telescopes with composite perfect objective lenses.

            chapter 3  : The division of telescopes into three particular kinds.

            chapter 4  : Telescopes of the first kind are without real images and represent objects upright.

            chapter 5  : Concerning the further perfection of telescopes of the first kind, by the addition of one

                               or more lenses  .


Sect. II, chapter 1  : The construction of telescopes of the second kind, with a convex objective and the inverse image .

Sect. II, chapter 2  : Concerning the further perfection of telescopes following the use of a single kind of glass.

Sect. II, chapter 3  : Concerning the further perfection of telescopes following the use of a two kinds of glass.


Sect. III, chapter 1  : The construction of telescopes of the third kind, for which objects again are represented erect.

Ian Bruce. Sept. 16th, 2019 latest revision. Copyright : I reserve the right to publish this translated work in book form. However, if you are a student, teacher, or just someone with an interest, you can copy part or all of the work for legitimate personal or educational uses. Please feel free to contact me if you wish, especially if you have any relevant comments or concerns about this work. My email address can be constructed from the information at the bottom of the introductory page of this website.