Though one may come across references on the web to the hippogriff (or sometimes "hippogryph") being the "Greek symbol of love", this is not the case— because the hippogriff is NOT GREEK, nor is it even mythological or folkloric. The Hippogriff is in fact the creation of a single man, a Renaissance poet by the name of Ludovico Ariosto (1474-1533)  in his poem Orlando Furioso. The first version of Orlando Furioso appeared in 1516. Minor revisions were made in the 1521 second edition, and major changes in the definitive and third edition published in 1532, a year before Ariostoís death. Yet even before the definitive edition, the poem was well known throughout Italy and subsequently in France, Spain and eventually England, acclaimed by critics as a modern epic.
The hippogriff first appears in Canto IV of his Orlando Furioso:
No empty fiction wrought by magic lore,
But natural was the steed the wizard pressed;
For him a filly to griffin bore;
Hight hippogryph. In wings and beak and crest,
Formed like his sire, as in the feet before;
But like the mare, his dam, in all the rest.
Such on Riphaean hills, though rarely found,
Are bred, beyond the frozen ocean's bound.
Thus, the original hippogriff is the offspring of a gryphon and a mare. Ariosto was likely inspired to create this creature by a few lines from Virgilís eighth Eclogue:
As horses and griffons were commonly reputed to be mortal enemies , Virgilís quip about griffons and mares is meant to denote something impossible (or which should be impossible), and it is from Virgilís comment that Ariosotoís hippogriff is born. Thus, the hippogriffís only real connection to Greek myth is its parentage by a griffon (though Virgil is a Roman writer of the first century B.C., the griffon itself dates from much earlier on, appearing in art from ancient Greece and Crete, as well as that from various Middle-Eastern cultures ) and by the its resonance with the image of the Pegasus, which appears in Greek myths of Bellerophon and of Perseus 
 For further information on Ariosto see here
 Marianne Shapiro, The Poetics of Ariosto (Detroit: Wayne State UP, 1988) 111.
Online resources suggest similar sources and translations:
We lovers look for? soon shall we see mate
Griffins with mares, and in the coming age.
Shy deer and hounds together come to drink."
Virgil. The Eclogues. The Internet Classics Archive. Ed. Daniel C. Stevenson. 22 Feb 2005. http://classics.mit.edu/Virgil/eclogue.mb.txt
 Jorge Luis Borges, The Book of Imaginary Beings, trans. Norman Thomas di Giovanni (Middlesex: Penguin 1969) 79.(also available online: Fantastic Zoology: A graphical interpretation of J.L. Borges Book of Imaginary Beings)
Florence McCulloch, Medieval Latin and French Beastiaries (Chapel Hill: University of North Carlina Press, 1962) 123.
"The History Behind the Gryphon". 22 Feb 2005. http://www.angelfire.com/sd/shedevil/gryphonhistory.html
 Hugh Lloyd-Jones, Mythical Beasts (London: Duckworth, 1980) 28.
Michael D. Winkle, "Ears of the Gryphon." A Gryphon Newsletter 1.2 (2001). The New, Improved Eyrie. 22 Feb 2005. http://www.oocities.org/laxaria/eyrie1b.html
 Marianne Shapiro, The Poetics of Ariosto (Detroit: Wayne State UP, 1988) 111-22.
Albert Russell Ascoli, Ariostoís Bitter Harmony: Crisis and Evasion in the Italian Renaissance (Princeton, N.J.: Princeton UP 1987) 246-57.