Proportion
“numbers proportional”
idea · 2 works · 3 mentions · 11 anchored passages
Numbers are proportional · analogia · analogy · comparison or proportion · ex aequali · in proportion · proportional magnitudes · that proportion
in the texts
Elements
The central relation of Book VII: numbers are proportional when the first is the same multiple, part, or parts of the second as the third is of the fourth; extensively used and proved throughout the propositions.
Numbers are proportional when the first is the same multiple, or the same part, or the same parts, of the second that the third is of the fourth.
and, if the number produced from the first and fourth be equal to that produced from the second and third, the four numbers will be proportional.
If four numbers be proportional, they will also be proportional alternately.
Timaeus
The mathematical relation binding the four elements together into a single cohering cosmic body, termed analogia in Greek.
But since solidity was sought for the universe, and solid things are never joined by one middle term but always by two, it so came about that the god placed water and air between fire and earth, and set them in due relation to one another and joined them by proportion, so that, as fire stands to air, so air should render itself to water, and as air stands to water, so water should render itself to earth.
This is best accomplished by what in Greek is called analogia, and in Latin (for one must venture, since these terms are now for the first time coined by us) may be called comparison or proportion.
For when, of three things — whether numbers, or figures, or any kinds whatsoever — it comes about that the middle is so related to the first in proportion as the last is to it, and conversely, that as the last stands to the middle, so the middle stands to the first, then that which is the middle becomes at once first and last, while the last and the first become middle;