New Elements of Geometry

Cover New Elements of Geometry
New Elements of Geometry
Seba Smith
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The shaded circumference is seen to consist of twelve units. And nine is three-fourths of twelve ; therefore the area equals three- fourths of the circumference.
In the arithmetical calculation of » the same square, the diameter or side of the square is 8, and 8 squared or multiplied by itself gives 9 for the area. And 3, one side, multiplied by 4, the number of sides, gives 12 for circumference.
Area therefore equals three-fourths cf the circumference, in num- bers as well as in magnitude.
90
...PART SECOND.
iil^Miii m ,.'i i''i| !. , „„.ii ••..,( l«^=■ ' PROPOSITION IV.
In the square whose diameter is four units, the area equals the circumference.
The white square in the diagram is seen to have four units for diameter and sixteen units for area. The shaded circumference is also seen to consist of sixteen units. The area therefore equals the circumference.
In the arithmetical calculation of the same square, the side is 4, which being multipKed by itself produces 16 for area.


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