gothic cathedrals pg 18

Gothic Cathedrals Pg 18

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Pg 38

The abacus was one of the earliest calculating devices, a 'step-up' from the more primitive counting board. This is a Roman example (note the Roman numerals), and earlier versions were developed in China.

Counting boardPg 43

SO MUCH EASIER!!!

Imagine trying to do calculus with these!!!

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St. Thomas Aquinas- The Scholastic (Pg 61)

Pg 85

The Gregorian calendar modified the Julian calendar's regular cycle of leap years, years exactly divisible by four, including all centurial years, as follows:Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year.In addition, it changed in the mean length of the calendar year from 365.25 days (365 days 6 hours) to 365.2425 days (365 days 5 hours 49 minutes 12 seconds), a reduction of 10 minutes 48 seconds per year.

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Portolani map Pg 96

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The treaty with the signature of the sovereign of Spain and Portugal.

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Pg 135

A neume is the basic element of Western and Eastern systems of musical notation prior to the invention of five-line staff notation. The word is a Middle English corruption of the ultimately Greek word for breath.

Pg 143

A Gregorian Chant on Youtube: http://www.youtube.com/watch?v=kK5AohCMX0U

Pérotin and Leonin.

Ma Fin est Mon Commencement on YouTubehttp://www.youtube.com/watch?v=WLEmVxqye4g

(Pg 173)Go here (http://www.thehistoryblog.com/archives/13433) if you want a cool story on the “demon” circled in red in the painting…

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Pg 186

“During this era, artists were exploring mathematical perspective for the first time, and the checkerboard pattern on the floor was a kind of ostentatious display of prowess.”From Quick History: Checkerboard Floors

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Pg 194

Ariel view of the floor in Flagellation

The rhombicuboctahedron, has eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. (Note that six of the squares only share vertices with the triangles while the other twelve share an edge.)The diagram on the right is if you laid it all out.

Pg 213

Vesalius, pg. 233