Proposition VIII.19 — Between two similar solid numbers there fall two mean propor…

Proof

For similar solid numbers

ab c

and

d e f

: the two means are

ab f

and

a e f

(or symmetric variants); together they give a continued proportion in triplicate ratio.

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Depends on (2)

VIII.12Proposition VIII.12Between two cube numbers there are two mean proportional numbers, and the cube has to the cube the ratio triplicate of…
VIII.18Proposition VIII.18Between two similar plane numbers there is one mean proportional number, and the plane number has to the plane number…

Required by (dependents) (2)

VIII.21Proposition VIII.21If two mean proportional numbers fall between two numbers, the numbers are similar solid numbers.
VIII.27Proposition VIII.27Similar solid numbers have to one another the ratio which a cube number has to a cube number.

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