Proof
For cubes , : the two means are and , and
is the triplicate of .
Knowledge graph · drag to pan, scroll to zoom, click a node to navigate
Full neighborhood
Depends on (4)
- 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…
- VII.19Definition VII.19A cube number is equal multiplied by equal and again by equal, or a number which is contained by three equal numbers.
- V.10Definition V.10When four magnitudes are continuously proportional, the first is said to have to the fourth the triplicate ratio of…
Required by (dependents) (5)
- VIII.15Proposition VIII.15If a cube number measure a cube number, the side will also measure the side; and if the side measure the side, the cube…
- VIII.19Proposition VIII.19Between two similar solid numbers there fall two mean proportional numbers, and the solid number has to the solid…
- VIII.23Proposition VIII.23If four numbers be in continued proportion, and the first be cube, the fourth will also be cube.
- VIII.25Proposition VIII.25If two numbers have to one another the ratio which a cube number has to a cube number, and the first be cube, the…
- IX.8Proposition IX.8If as many numbers as we please beginning from a unit be in continued proportion, the third from the unit will be…
Discussion
No replications, contradictions, or comments registered yet for this claim.
Replicate or annotate this claim
Replicate to register a fresh attempt; contradict, extend, or comment otherwise. Authors can post a claim-retraction with the reason taxonomy from RRP-0020.
Sign in with ORCID to annotate this claim.