letter phi. Over time, the symbol changed to and . The latter symbol further evolved into , then , and eventually changed to under the influence of the Latin word mille "thousand". According to Paul Kayser, the basic numerical symbols were , , and (or ) and the intermediate ones were derived by taking half of those (half an is , half a is and half a is ). Classical Roman numerals The Colosseum was constructed in Rome in CE 72–80, and while the original perimeter wall has largely disappeared, the numbered entrances from (23) to (54) survive, to demonstrate that in Imperial times Roman numerals had already assumed their classical form: as largely standardised in current use. The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation - while is used for 40, is avoided in favour of : in fact, gate 44 is labelled . Use in the Middle Ages and Renaissance Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: , , , , and so on. Since the Middle Ages, a "" has sometimes been substituted for the final "" of a "lower-case" Roman numeral, such as "" for 3 or "" for 7. This "" can be considered a swash variant of "". Into the early 20th century, the use of a final "" was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written. Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called "medieval Roman numerals". Some simply substitute another letter for the standard one (such as "" for "", or "" for ""), while others serve as abbreviations for compound numerals ("" for "", or "" for ""). Although they are still listed today in some dictionaries, they are long out of use. Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters , , , , , , and . By putting these letters together, the reader would obtain a number, usually indicating a particular year. Modern use By the 11th century, Arabic numerals had been introduced into Europe from