Proof
counts the units in a -many sum of 's;
counts the units in an -many sum of 's. Both equal by
VII.5 applied to the unit.
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Depends on (3)
- VII.5Proposition VII.5If a number be a part of a number, and another be the same part of another, the sum will also be the same part of the…
- VII.15Proposition VII.15If a unit measure any number, and another number measure any other number the same number of times, then, alternately,…
- VII.15Definition VII.15A number is said to multiply a number when that which is multiplied is added to itself as many times as there are units…
Required by (dependents) (3)
- VII.17Proposition VII.17If a number by multiplying two numbers make certain numbers, the numbers so produced will have the same ratio as the…
- VII.18Proposition VII.18If two numbers by multiplying any number make certain numbers, the numbers so produced will have the same ratio as the…
- IX.4Proposition IX.4If a cube number by multiplying a cube number make some number, the product will be cube.
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