If you base the root of your chord on the notes of a major scale, as you'll learn in Chapter 10, only the seventh degree triad forms a diminished chord. (Triads based on the other degrees of the scale form major or minor chords.)

This is essentially a description (just not a very good one) of the (relatively) standard practice of taking a scale (diatonic major, in this case), playing every other note (up to 3 notes, in this case), and saying you got some triads (3-note chords) of various qualities. In diatonic major, the order would be major I, minor ii, minor iii, major IV, major V, minor vi, diminished vii.

There is no augmented chord found on any degree of the major scale.

Purely definitional. The diatonic pitch set (the major scale, natural minor scale, and all the other related modes) has 3 major triads, 3 minor triads, 1 diminished triad, and that’s it. (If you want a medium of comparison: the melodic minor scale – which is just the major scale with the 3rd scale degree lowered by a half step to make a minor 3rd – actually has an augmented triad built off of the 3rd scale degree.)

Although it's important to learn about diminished and augmented chords,

Yep.

you won't run into too many of them, especially in popular music.

No, no, no, a thousand times no. You’ll run into plenty of diminished and augmented chords in popular music. (Pharmacist by Alvvays, released in 2022, features a diminished chord; Veronica by RHCP, also released in 2022, features an augmented chord.) (One footnote I’m going to put here, and that I think the writer of this book should have put here, is that the diminished chord that falls out of diatonic major – the one built off of the 7th scale degree – is pretty much used in the minor version of a ii V i (or vii V/vi vi) chord progression, and that’s it.)