Which implies that the tiny Hyracotherium gradually changed into a series of other species until the lineage evolved into the modern day horse, Equus.
indicating that ancestral lineages split into two descendant lineages at each clade (branch point). By definition, when an ancestral taxon splits into two new taxa, the ancestor becomes extinct, even if one of the new sister taxa is virtually identical to the original.
Using this model, it is incorrect to say that Equus evolved from Hyracotherium. One can say only that the two genera share a common ancestor, even though one of the two taxa is extinct.
One also cannot say that early hominid species gave rise to humans. The most we can say is that all hominids--fossil or extant--share a common ancestor.
Below, a cladogram of Hominids...