Kutepov, Rubanov – Problems in Geometry

We now come to a problem book in Geometry by A. Kupteov and A. Rubanov titled Problems in Geometry. Earlier we had seen two problem books in Plane Geometry and Solid Geometry in the Science for Everyone Series.

From the Preface:

The book contains a collection of 1351 problems (with answers) in plane and solid geometry for technical schools and colleges. The problems are of varied content, involving calculations, proof, construction of diagrams, and determination of the spatial location of geometrical points. It gives sufficient problems to meet the needs of students for practical work in geometry, and the requirements of the teacher for varied material for tests, etc.

The book was translated from the Russian by Oleg Meshkov and was edited by Leonid Levant. Mir Publishers published this book first in 1975

You can get the book here.

All credits to the original uploader.



1. The Ratio and Proportionality of Line Segments,
Similarity of Triangles 7
2. Metric Relationships in a Right-Angled Triangle 10
3. Regular Polygons, the Length of the Circumference
and the Arc 15
4. Areas of Plane Figures 17


5. Solving Right-Angled Triangles 22
6. Solving Oblique Triangles 29
Law of Cosines 29
Law of Sines 31
Areas of Triangles, Parallelograms and
Quadrilaterals 32
Basic Cases of Solving Oblique Triangles 34
Particular Cases of Solving Oblique Triangles 34
Heron’s Formula 35
Radii r and R of Inscribed and Circumscribed Circles and the Area S of a Triangle 36
Miscellaneous Problems 37


7. Basic Concepts and Axioms. Two Straight Lines in Space 43
8. Straight Lines Perpendicular and Inclined to a Plane 46
9. Angles Formed by a Straight Line and a Plane  52
10. Parallelism of a Straight Line and a Plane 55
11. Parallel Planes  59
12. Dihedral Angles. Perpendicular Planes 63
13. Areas of Projections of Plane Figures 67
14 Polyhedral Angles 69


15. Prisms and Parallelepipeds 71
16. The Pyramid 77
17. The Truncated Pyramid 81
18. Regular Polyhedrons 84
19. The Right Circular Cylinder 86
20. The Right Circular Cone 89
21. The Truncated Cone 93


22. Areas of Parallelepipeds and Prisms 97
23. Areas of Pyramids 102
24. Areas of Truncated Pyramids 105
25. Areas of Cylinders 108
26. Areas of Cones Ill
27. Areas of Truncated Cones 115


28. Volumes of Parallelepipeds 118
29. Volumes of Prisms 122
30. Volumes of Pyramids 127
31. Volumes of Truncated Pyramids 133
32. Volumes of Cylinders 137
33. Volumes of Cones 141
34. Volumes of Truncated Cones 145


35. Spheres 149
36. Areas of Spheres and Their Parts 152
37. Volumes of Spheres and Their Parts 155
38. Inscribed and Circumscribed Spheres 159


39. Polyhedrons 164
40. Round Solids 168
41. Areas and Volumes of Prisms 172
42. Areas and Volumes of Pyramids ……… 176
43. Areas and Volumes of Round Solids . 181
Answers 187

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18 Responses to Kutepov, Rubanov – Problems in Geometry

  1. Thiago says:

    “You need to be a premium member in order to download this file.”

    Can’t download this and other books posted recently.


  2. Ashish says:

    I have gained access to the following rare translated Russian books:
    1.A Laboratory Course in Optics-I E Irodov
    2.Laboratory Manual for Electromagnetism experiments-I E Irodov
    3.Volume 1 and 2 of D V Suvikhin’s Course in General Physics series
    4.Volume 1,2,3 of D V Suvikhin’s Problems in Undergraduate Physics series
    5.About 50 brilliant mathematics articles from the journal Kvant.
    and the following untranslated Russian books (in .djvu format)
    1.Macroscopic Physics-I E Irodov
    2.Quantum Mechanics: Basic Laws-I E Irodov
    3.Wave Processes-I E Irodov
    4.Remaining books of both series of books D V Suvikhin(see 2 &3 above)
    5.Entire General physics course by Savi’elev and corresponding problem books.
    6.Mathematics for Engineering Entrance Exams-M Potapov
    Query 1 Please inform me if you have English versions of any of these untranslated books.
    Query 2 Can anyone tell me is there any kind of a shop/company in New Delhi which can translate Russian technical documents into English and their approx. fees?
    Query 3 I have translated with the help of google translate all the problems in physics from the Kvant magazine (2000-2008 all editions). Is anyone interested?
    My email id is ashishdv@gmail.com.


    • damitr says:

      No, as of now we do not have translated works of any of these books. Maybe you can check with the Russian embassy, about who can translate books for you. Maybe we can set up a project for translations.



  3. Ashish says:

    Also some of Physics articles of the Kvant magazine………..


  4. Ashish says:

    Its ashishdv28@gmail.com….Correct that…


  5. gnv64 says:

    Hi damitr!
    I have uploaded this book:

    First Aid
    By V.M.Buyanov
    Translated from the Russian by Elena Koltsova
    Mir Publishers | 1985 | ISBN – N/A | PDF | 230 pages | 7.2 mb
    scanned to PDF by me

    First aid is a combination of the emergency medical measures used in case of sudden ill-ness or accident. The first aid rendered on the spot or as the victim is being transported to medical facilities may vary and is classified as follows:
    (1) unskilled first aid rendered by a layman who often has none of the necessary means or medicines;
    (2) qualified first aid (before the arrival of a doctor) rendered by a specially trained medical worker (medical technician”, nurse, laboratory or dental technician);
    (3) first aid rendered by a doctor who has the necessary instruments, apparatus, medicines, blood and blood substitutes, and so on at his disposal.
    The textbook deals with general concepts and essentials of First Aid in various accidents and sudden illnesses. General problems discussed in the book include the concepts of asepsis and antisepsis, the principles of applying bandages and basic aspects and methods of resuscitation. First Aid in haemorrhages, wounds, injuries to the soft tissues and bones, electric shock, heat- and sun-stroke, poisoning, acute surgical and non-surgical diseases, and emergency labour are dealt with in detail.

    Introduction 9
    Chapter I. Essentials of Antisepsis and Asepsis 13
    Chapter 2. Techniques for Applying Bandages 31
    Chapter 3. General Principles for Rendering First Aid 54
    Chapter 4. Shock 75
    Chapter 5. Principles and Methods of Resuscitation 80
    Chapter 6. First Aid for Haemorrhages 101
    Chapter 7. First Aid in Wounds Wounds 125
    Chapter 8. First Aid in Injuries to the Soft Tissues, Joints and Bones 138
    Chapter 9. First Aid for Burns and Frostbite 152
    Chapter 10. First Aid for Accidents and Sudden Illness 161
    Chapter 11. Care of Patients: Elements of Rendering First Aid 200
    Supplement 1. Table of Common Poisons and Their Antidotes 206
    Supplement 2. Specific (Antidote) Treatment of Acute Poisoning 211
    Supplement 3. Hypothetical Situations for Studying the Principles of First Aid: Tasks for Self-control 214
    Subject Index 224


  6. somen says:

    hi damitri
    when u will complete whole series of little mathematics library.


  7. asd says:

    hope next turn is of physics problems!


  8. Siddharth says:

    Do you have the book
    Mathematical Analysis – A brief course for engineering students
    by A.F.Bermant & I.g. Aramanovich (MIR Publishers) ?


    • damitr says:

      This we have, but not scanned as yet.



      • Siddharth says:

        Which scanner (company) & softwares (OCR, bookmark) have you used for creating e-books?


      • pranjal gupta says:

        Can u please get the book A brief course for engineering students
        by A.F.Bermant & I.g. Aramanovich (MIR Publishers) scanned


        • Siddharth says:

          Hi pranjal
          Till damitr posts a good quality version of this e-book, there is a link of not-so-good quality version uploaded by me. Just open the latest post titled “Update: Books in Comments” & scroll down the page. You will find many Soviet books uploaded by me


  9. somen says:

    hi damitr,
    Do you have book “HIGH SCHOOL MATHEMATICS “BY GN YAKOVLEV MIR PUBLISBER vol 1 and 2 .This book is mentioned in goodreads with three star rating.


  10. Srinivas says:

    Hi Damitr

    Firstly, I thank you and all those who have contributed for the terrific job that you have started and have been diligently doing for such a long time. Hats off to your commitment.

    So, far I have been a beneficiary of your good work. Now, I feel it is high time I contribute my two cents and express my gratitude to this wonderful forum.

    I have a collection of untranslated russian books in high school physics and math along with a collection of olympiad problems in physics. I am sure there are many who would benefit from the translated version of the material referred above.

    Pl mail me on poluru@gmail.com and we could take it further.

    Thank you once again!


  11. A95M says:

    The 4 shared link downloads a corrupted file….please update the internet archive link


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