Slaves could certainly have children. A male and female slave are certainly capable of reproducing. Did you need a diagram? ;-)Your source is a silly one, it says from the start " Only children of slaves or non-Muslim prisoners of war could become slaves, never a freeborn Muslim"
How a slave can have children while they're slaves, also how only non-muslim prisoners could become slaves while the same source says
"a Muslim slave is equal to a Muslim freeman in religious issues and superior to the free non-Muslim"
Only a non-Muslim could become a slave, but a slave could convert and become a Muslim slave. This, too, you couldn't figure out? Speaking of silly...