Adverb
According to the rules or laws of geometry.
Source: Webster's dictionaryWhoever ... proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured. Albrecht Dürer
We seem to inhabit a universe made up of a small number of elements-particles-bits that swirl in chaotic clouds, occasionally clustering together in geometrically logical temporary configurations. Timothy Leary
Whence a geometrically moving point approaching a fixed one has its velocities proportionate to its distances from the fixed one. John Napier
To decrease geometrically is this, that in equal times, first the whole quantity then each of its successive remainders is diminished, always by a like proportional part. John Napier
There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? Pierre de Fermat
"Malthus,", says Vice President Al Gore in Earth in the Balance, "was right in predicting that the population would grow geometrically." Al, as the father of four children, should know. P. J. O'Rourke