Make a Triangularity program valid
Triangularity, 127 bytes

.......).......
......2)1......
...../)IL^.....
....f)rMD@_....
...)2)1/)IL^...
..f+`"'.'*"+E..
.DWReD)2s^)Its.
D+@sh+s+})10cJ.


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Explanation

Removing the characters that make up for the padding, we get the following program:

)2)1/)IL^f)rMD@_)2)1/)IL^f+`"'.'*"+EDWReD)2s^)ItsD+@sh+s+})10cJ


... Which is quite length-ish, right? Let's break it down into pieces.

Generating the integers [0 … √len(input))

)2)1/)IL^f)r – Subprogram #1.
)            – Creates a new stack entry, equal to 0. This must precede any integer
               literal, because each character in '0123456789' isn't parsed on its
               own as a literal, but rather they are commands which multiply the ToS
               by 10 and add the value of their digit equivalent. 
 2           – ToS * 10 + 2 = 2.           || STACK: [2]
  )1         – The literal 1.              || STACK: [2, 1]
    /        – Division.                   || STACK: [1 / 2] = [0.5]
     )I      – Get the input at index 0.   || STACK: [0.5, input]
       L     – Length.                     || STACK: [0.5, len(input)]
        ^    – Exponentiation.             || STACK: [len(input) ** 0.5]
         f   – Trim decimals.              || STACK: [int(len(input) ** 0.5)] 
          )r – Create the list [0 .. ToS). || STACK: [[0 ... int(len(input) ** 0.5))]


Generating the dots

MD@_)2)1/)IL^f+`"'.'*"+E – Subprogram #2.
MD                       – For each integer in the range, run some code on a separate
                           stack, preinitialised to two copies of the argument.
  @_                     – Increment and negate the ToS.
    )2)1/)IL^f           – The square root of the length of the input, again.
              +          – Add the two.
               `         – And cast the integer given to a string.
                "'.'*"+  – Prepends the literal "'.'*" to the string representation.
                       E – Evaluate as a Python expression (basically string repetition).


Trimming the characters at the front

DWReD)2s^)It – Subprogram #3.
D            – Duplicate the result of the expression above.
 W           – Wrap the whole intermediate stack to an array.
  Re         – Reverse the stack and dump the contents separately onto the stack.
    D        – Duplicate the result.
     )2      – Push the literal 2.
       s^    – Swap and perform exponentiation.
         )It – Push the input and trim the characters before that index.


Trimming the characters at the end

sD+@sh+s+ – Subprogram #4.
s         – Swap the top two elements on the stack.
 D+       – Double. Push twice and add.
   @      – Increment.
    sh    – Swap the top two elements and trim the characters after that index.
      +   – Append the first set of dots.
       s+ – And prepend the second set of dots.


Ending the loop and pretty-printing

})10cJ – Subprogram #5.
}      – End the loop.
 )10   – Push the literal 10.
    c  – Convert from code-point to character (yields '\n').
     J – And join the result by newlines.