Full Idea
You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities.
Gist of Idea
I wish to go straight from cardinals to reals (as ratios), leaving out the rationals
Source
Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.270
A Reaction
Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc.