geometry postulates and common notions

postulate one

to draw a straight line from any point to any point

postulate two

to produce a finite straight line continuously in a straight linr

postulate three

to describe a circle with any centre and distance

postulate four

that all right angles are equal to one another

postulate five

that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side which are the angles less than two right angles

common notion 1

things which are equal to the same thing are also equal to one another

common notion one example

a=c

b=c

therefore a=b

common notion two

if equals be added to equals, the wholes are equal

common notion two example

a=c

a+b=b+c

common notion three

if equals be subtracted from equals, the remainders are equal

common notion three example

a+b=b+c

i already know b=b

therefore, if b is subtracted from both sides, a=c

common notion four

things which coincide with one another are equal to one another

common notion four example

corresponding parts perfectly touch corresponding parts

common notion five

the whole is greater than the part

common notion five example

a whole cookie is bigger than half a cookie