ummm ... Hippy you've described the why of the origin of the Gregorian calendar, with a bit other stuff mixed in.
Before the Gregorian calendar, people used the Julian calendar which was introduced by Julius Caesar to sort out the mess that the Roman Republican calendar had become.
The original Roman calendar started in March and had 10 months, 6 of 30 days and 4 of 31 days (giving a total of 304 days) with an uncounted gap between December and March. This was amended to add two extra months (January and February) and increased the total number of days in the year to 355.
When the Roman Republican calendar was March, May, July and October were left with 31 days, January, April, June, August, September, November and December all had 29 days leaving February with 28 days.
This means that the Roman calendar was basically a lunar calendar which came up 10.25 days short of the solar calendar, so to prevent it from getting too far out of step with the seasons an extra month of 27 or 28 days was added every two years between February 23rd and February 24th, and in historical times the last 5 days of February were dropped.
The calendar adopted by Julius Caesar allowed for 365 days in the year ... the extra days being added to the end of existing months but leaving February with 28 days. To get round the missing quarter of a day each year, an extra day was to be added to the year every 4th year, and in line with the original rule of the Roman calendar, it was added to February, but as an extra day during the month not at the end of the month.
There is a very long article in the Encyclopaedia Britannica about claendars, which is where I grabbed the information from, The link, if anyone is interested is
http://www.britannica.com/eb/article-59347/cal endar and the stuff about the Julian calendar is on page