This is no different from any decimal ...

But if I have the decimal number -345, this is
    -(3*10^2 + 4*10^1 + 5*10^0)
or
    -1 * (3*10^2 + 4*10^1 + 5*10^0)
or
    -3*10^2 + -4*10^1 + -5*10^0
or
    -3*10^2 - 4*10^1 - 5*10^0
and not
    -3*10^2 + 4*10^1 + 5*10^0
and similarly for numbers represented in sexagesimal base.

Negative numbers are only permitted in the degree column.

Unfortunately, if one has a d/m/s tuple  @dms = (3, 4, 5) one cannot negate it by writing -@dms. One has to negate each element:
    @neg_dms = map -1*$_, @dms;
or (-3, -4, -5). IIUC, the notation -3° 4' 5" is equivalent to the tuple (-3°, -4', -5") analogously to decimal notation. Klaf is describing and giving an example of base-60 subtraction with borrowing, but that is not fundamentally different from base-10 subtraction.

Update 1: Added the "Negative numbers ..." quote before the second paragraph for clarification, and various other minor wording changes and additions.

Update 2: Here's the Klaf subtraction example in terms of normalizing everything to decimal arc-seconds, doing a decimal subtraction and reducing arc-seconds to a d/m/s tuple:

c:\@Work\Perl\monks\thechartist>perl -wMstrict -le
"sub dms_2_secs {
   my ($degs, $mins, $secs) = @_;
   ;;
   return $degs * 3600 + $mins * 60 + $secs;
   }
 ;;
 sub secs_2_dms {
   use integer;
   ;;
   my ($secs) = @_;
   ;;
   my $degs = $secs / 3600;   $secs %= 3600;
   my $mins = $secs /   60;   $secs %=   60;
   ;;
   return $degs, $mins, $secs;
   }
 ;;
 my $klaf_arc_secs = dms_2_secs(83, 18, 21) - dms_2_secs(39, 41, 28);
 my @klaf_dms      = secs_2_dms($klaf_arc_secs);
 print qq{(@klaf_dms)};
"
(43 36 53)
[download]

(Update: The Klaf addition example also works correctly.) (Update: Moreover, the reversed subtraction  dms_2_secs(39, 41, 28) - dms_2_secs(83, 18, 21) yields the expected (-43 -36 -53) tuple.)

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