example for SPI EEPROM (25LC512 )?

Hello,
I am new at that forum and want to great everyone.

I want to use an external SPI EEPROM (25LC512). I found a library that supports that chip, but don’t know how to use it right. I2C is no option.
SPI EEPROM Library:
https://bitbucket.org/spirilis/spieep/wiki/Home
I want to save an 3d array ( "test(a)(b)(c)" - I cannot use square brackets here) with up to 10.000 lines, which equals 30.000 values. And all data is dedicated to one type of data. (uint16_t)
I have a 4x5 matrix keypad and an LCD display. With the keypad I input the values. There is not enough internal memory for my array. So I would like to store the values to an SPI EEPROM. Later on the values should be read and used by the Arduino to radio the values to an receiver which uses the values.
So, in the first part of the program, the values are written to the emprom and in another part, the values should be read.

I got an 25LC512 SPI IC chip. This IC can be used with SPI. Because of the amount of my data, I think I have to take care of page boundaries.
The mentioned SPI library at bitbucker was written for the 25LC512 IC but I didn’t succeed to use it. The SPIEEPROM tutorial at Arduino.cc didn’t take care about page boundaries, which may be important for my project.

For my project my Arduino just has to control the input of the values, show the values on the 2lines LCD display and send them to another Arduino.
Input, displaying and sending works fine, but I don’t know how to “talk” to the EEPROM. The values will be uint16_t. I would need an example to read and write to the EEPROM.

Can anyone help and post an example or any sketch that uses a similar IC, so I can see how to use SPI EEPROM? I just need an example how to use read and write correctly. The examples provides at the library site, didn’t help.
Maybe anyone can help and post some example code, so I can learn how to use it right.

Thanks in advance!