void setup(void) {
  Serial.begin(9600);
}

#define log_size 5
#define line_height 12
char *log_lines[log_size] = {"Hello", "World"};

void addToLog(char *text) {
  for(int i = log_size - 1; i > 0; i--) {
    log_lines[i] = log_lines[i-1];
  }
  log_lines[0] = text;
}

void printLog() {
  for(int i = 0; i < log_size; i++) {
    Serial.print(i);
    Serial.print(" ");
    Serial.println(log_lines[i]);
  }
}

void loop(void)
{
  char msg[20];
  sprintf(msg, "%d", millis());
  addToLog(msg);
  printLog();
  delay(1000);
}

0 1000
1 Hello
2 World

0 2001
1 2001
2 Hello
3 World