- •III. Give full answers:
- •IV. Ask questions in the model using the words suggested:
- •V. Make the sentences negative:
- •VI. Make the sentences impersonal using the noun-substitutes and modal verbs:
- •VII. Make the sentences more emphatic. Tarn active into Passive, if necessary.
- •VII. Translate the sentences identifying the grammar rules patterns involved:
- •I. Imperative.
- •Indefinite Tense-Aspect forms
- •VII. Emph. Именно (как раз) математики ( в самом деле, ведь) доказывают теоремы.
- •X. The verb “to do” functions.
- •I.Use the following sentences in your oral description of the ancient practical (empirical, experimental) geometry:
- •V. В математике много думают, рассуждают, доказывают, обосновывают.
VII. Translate the sentences identifying the grammar rules patterns involved:
One knows that Geometry started far back in antiquity from some very
modest beginnings and gradually grew to its presents enormous size. 2. People are aware that the nature, or inherent character of the subject had different connotation at different periods of its development. 3. Many observations in the daily lite of early man did lead to the geometric concepts of curves, surfaces and solids. 4. It was the construction of houses that suggested the notion of vertical, of parallel, and of perpendicular. One can multiply such examples almost indefinitely. 5. While we must not be certain, it does seem safe to assume that scientific geometry arose from practical necessity. 6. It was the Greeks who transformed Geometry into something vastly different from the set of empirical conclusions worked out by the ancient Egyptians and Babylonians. 7. Induction and deduction are different ways of reasoning. The former is mainly used in experimental science, while the latter is the major method of reasoning in mathematics. 8. People can hardly overemphasize the importance of Euclid’s “Elements”. 9. The theory of parallels did occupy geometers for over two thousand years. 10. Euclidean and non- Euclidean geometries are alternative ways geometrically two describe to physical space, both the former and the latter are consistent.
REVISION
(Similar revisions of all the Grammar rules studied should be done at the end of each term)
Summarize all the Grammar rules and verb “to do” functions so far studied.
I. Imperative.
Suppose (Let us suppose) we have a theorem. Prove it deductively. Let her
(him, them) do it.
II. Дедуктивно и строго доказывают (должны доказывать) теоремы математики.
Indefinite Tense-Aspect forms
Mathematicians prove (must prove) theorems deductively and
Present { rigorously.
Theorems are proved (must be proved) deductively and rigorously.
Mathematicians proved (were to prove, had to prove) theorems
Past { deductively.
Theorems were proved (were to be proved, had to be proved)
deductively.
A deductive proof is (was) much spoken and written about.
A rigorous and elegant deductive proof is (was) looked at with
admiration.
III. Questions. Who proves (must prove) theorems? Who proved (was to prove, had to prove) theorems? What do (did) mathematicians do? How do (did) mathematicians prove theorems? Mathematicians prove(d) theorems, don’t (didn’t) they? Do (Did) mathematicians prove theorems deductively or inductively? What is a deductive proof? Is it difficult to prove theorems deductively?
IV. Negations. Don’t prove theorems that way. Don’t let him (her, them) prove theorems that way. Let us not prove theorems that way. Mathematicians do not (did not) prove theorems that way. No mathematicians proves theorem s that way. Don’t (Didn’t) mathematicians prove theorems deductively? Mathematicians prove (d) nothing that way. Mathematicians prove (d) theorems that way nowhere.