What decides chords in a scale?

was going through a book (from: http://www.true-piano-lessons.com/piano-player.html), which I like.

There it is written:

Within  every  major  or  minor  scale,  there  are  seven  chords    —  one  for  each  tone  of  the  scale,  and  numbered  accordingly.    As  an  example,  if  you  were  to  number  and  name  the  chords  of  the  C-­‐major  scale,  you  would  get  the  following:  the  I-­‐chord is  C  Major,  the  ii-­‐chord  is  D  Minor,  the  iii-­‐chord  is  E  Minor,  the  IV-­‐chord  is  F  Major,  the  V-­‐chord  is  G  Major,  the  vi-­‐chord  is  A  Minor,  and  the  vii°-­‐chord  is  B  Diminished.  Every  major  scale  has  the  same  pattern  of  major,  minor,  and  diminished  triads....

How are these patterns decided? If I just start and play the major keys in 1-5-8 pattern I will just get all the major chords. As described below:

 

C

?

D

?

E

F

?

G

?

A

?

B

C

*

*

*

C#

*

*

*

D

*

*

*

D#

*

*

*

E

*

*

*

F

*

*

*

F#

*

*

*

G

*

*

*

G#

*

*

*

A

*

*

*

A#

*

*

*

B

*

*

*

There must be some logic behind it. What is it?