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Página 2
... these statements is the contrapositive of the other . Two Theorems are said to be converse , each of the other , when the hypothesis of each is the conclusion of the other . Thus , If C is D , then A is 2 ELEMENTARY GEOMETRY .
... these statements is the contrapositive of the other . Two Theorems are said to be converse , each of the other , when the hypothesis of each is the conclusion of the other . Thus , If C is D , then A is 2 ELEMENTARY GEOMETRY .
Página 3
... converse of the original Theorem . The truth of a converse is not a logical consequence of the truth of the original Theorem , but requires independent investigation . Thus , supposing it were true that if a man is a Spaniard his hair ...
... converse of the original Theorem . The truth of a converse is not a logical consequence of the truth of the original Theorem , but requires independent investigation . Thus , supposing it were true that if a man is a Spaniard his hair ...
Página 4
... converse of each of two such Theorems is the contrapositive of the other . Another example , of frequent occurrence in the elements of Geometry , is of the following type : If A is greater than B , C is greater than D. If A is equal to ...
... converse of each of two such Theorems is the contrapositive of the other . Another example , of frequent occurrence in the elements of Geometry , is of the following type : If A is greater than B , C is greater than D. If A is equal to ...
Página 17
... converse , contrapositive , giving examples of each . 3. State the Geometrical Axioms . 4. What is meant by the axiom of the rule of Identity ? 5. State the fact that " all geese have two legs " in the form of a theorem , with ...
... converse , contrapositive , giving examples of each . 3. State the Geometrical Axioms . 4. What is meant by the axiom of the rule of Identity ? 5. State the fact that " all geese have two legs " in the form of a theorem , with ...
Página 40
... converse and contrapositive theorems . 3. Apply Theorem 7 to find the height of a tower . 4. Prove Theorem 6 in the manner of Theorem 8 . 5. Why cannot Theorem 15 be proved in the same manner as Theorem 5 ? 6. Prove that only one ...
... converse and contrapositive theorems . 3. Apply Theorem 7 to find the height of a tower . 4. Prove Theorem 6 in the manner of Theorem 8 . 5. Why cannot Theorem 15 be proved in the same manner as Theorem 5 ? 6. Prove that only one ...
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Términos y frases comunes
AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
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