Vocabulary Notes

application – alkalmazás

Archimedes – Arkhimédész

assume v – feltesz, feltételez

axiom on parallels – párhuzamos egyenesek axiómája

contain v – tartalmaz

consist v – áll vmiből

proof – bizonyítás

derive v – származik, ered

erect v – létesít

Euclid – Euklidész

habit – szokás

locate v – helyet megállapít

Plato – Platón

Pythagoras – Püthagorasz

volume – tömeg,

Elements – Elemek

non-Euclidean geometry – differenciálgeometria

Pythagorean – Pütagorasz követője

Exercises

I. According to the text, are the following statements true or false?

1. Geometry is the Greek name for the science which the early Egyptians began and developed about 5000 years ago.

2. The most important of the early Greek philosophers and teachers was Archimedes who was born about 569 BC.

3. Plato, who lived more than 100 years before Pythagoras, was primarily a mathematician.

4. The Elements of Euclid has been used as a basis for all textbooks on geometry since his time.

5. In the 20^th century the Russian mathematician Lobatchevsky founded elliptic geometry.

6. Riemann assumes that no straight line can be drawn which will not meet any other straight line.

II. Find in the text the following words and word combinations. Guess their meanings. Make up your own sentences with them.

to be derived from, to be able to do smth, to be interested in smth, to perfect, to found, to be divided into, primarily, in connection with smth, used to do smth, accurately, to discover, to be based on smth.

III. Answer the following questions on the text:

1. Who began and developed geometry as a science?

2. What is the origin and meaning of the word geometry?

3. What did the geometry known to the Egyptians principally consist of?

4. Who developed and perfected the proofs of the Egyptians?

5. Who was the most important of the early Greek teachers and what was he famous for?

6. Why was Plato interested in geometry?

7. What textbook was used as a basis for all textbooks on geometry and who was its author?

8. How long was Euclidean geometry the ruling theory?

9. Who is the founder of non-Euclidean geometry?

10. How do we call non-Euclidean geometry by Lobachevsky?

11. Who developed the third system of geometry and what did it assume?

IV .Change the sentences to negative and to question form:

1. The geometry known to the Egyptians consisted principally of rules and formulas.

2. The best known name in connection with geometry is Euclid.

3. The Elements of Euclid have been used as a basis for all textbooks on geometry since his time.

4. The 3^rd system of geometry was developed by Riemann.

V. Find English equivalents to the given sentences in the text.

1. Az egyiptomiakat, főképp, a szabályok gyakorlati felhasználása érdekelte.

2. A geometria nem a gyakorlati felhasználása miatt érdekelte őt, hanem a logika miatt, amelyet a bizonyítások tartalmaztak.

3. Attól az időtől fogva Euklidész Elemei minden mértankönyvnek az alapja.

4. Ez azon a feltételezésen alapszik, hogy a párhuzamos egyenesek axiómája helytelen és egy ponton keresztül számtalan mennyiségű egyenest lehet meghúzni, amelyek párhuzamosak lesznek az adott egyeneshez.