Axiom nd posulate

Post on 17-Jul-2015

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Transcript of Axiom nd posulate

EUCLID”S EUCLID”S DEFINATIONSDEFINATIONSAXIOMSAXIOMS && POSULATEPOSULATE

SS

EUCLIDEUCLIDHE WAS ATEACHEROF HE WAS ATEACHEROF

MATHEMATICS AT ALEXENDRIA MATHEMATICS AT ALEXENDRIA IN EGPT,COLLECTED ALLTHE IN EGPT,COLLECTED ALLTHE KNOWN WORK AND ARRANGE IT KNOWN WORK AND ARRANGE IT IN HIS FAMOUS IN HIS FAMOUS TREATISE,CALLED “ELEMENT”. TREATISE,CALLED “ELEMENT”. HE DRIVED ELEMENT INTO HE DRIVED ELEMENT INTO THIRTEEN CHAPTERS,EACH THIRTEEN CHAPTERS,EACH CALLED A BOOK THESE CALLED A BOOK THESE INFLUENCED THE WHOLE WORLD INFLUENCED THE WHOLE WORLD UNDERSTNDING OF GEOMETRY UNDERSTNDING OF GEOMETRY FOR GENRATIONS TO COME . FOR GENRATIONS TO COME .

77 AXIOMS AXIOMS

THINGS WHICH ARE EQUAL TO HE SAME THING ARE EQUAL TO ONE ANOTHER

IF EQUALS ARE ADDED TO, EQUALS , THE WHOLES ARE EQUAL .

IF EQUALS ARE SUBTRACTED FROM EQUALS , THE REMAINDERS ARE EQUAL .

THINGS WHICH CONCIDE WITH ONE ANOTHER ARE EQUAL TO

ONE ANOTHER .

THE WHOLES IS GREATER THAN THE PART .

THINGS WHICH ARE DOUBLE OF THE SAME THINGS ARE EQUAL TO ONE ANOTHER .

THINGS WHICH ARE HALVES OF THE SAME THINGS ARE EQUAL TO ONE ANOTHER .

5 5 POSULATES POSULATES

A STRAIGHT LINE MAY BE DRAWN FROM ANY ONE POINT TO ANY ANOTHER POINT .

A TERMINATED LINE CAN BE A TERMINATED LINE CAN BE PRODUCED INDEFINATELY . PRODUCED INDEFINATELY .

A CIRCLE CAN BE DRAWN WITH ANY CENTER AND

ANY RADIOUS .

ALL RIGHT ANGLES ARE EQUAL TO ONE ANOTHER .

IF A STRAIGHT LINE FALLING ON 2 STRAIGHT LINES MAKE THE INTERIOR ANGLES ON THE SAME SIDE OF IT TAKEN TOGETHER LESS THEN 2 RIGHT ANGLES,THEN THE 2 STRAIGHT LINES,IF PRODUCED INDEFINITELY,MET ON THAT SIDE ON WHICH THE SUM OF ANGLES IS LESS THAN 2 RIGHT ANGLES.