at vs by

at

prep
  • Indicates a means, method, or manner. 

  • (also as at; before dates) On a particular date. 

  • Occupied in (activity). 

  • In a state of. 

  • On the subject of; regarding. 

  • In, near, or in the general vicinity of a particular place. 

  • Denotes a price. 

  • Because of. 

  • Bothering, irritating, causing discomfort to 

  • Indicates a position on a scale or in a series. 

  • Holding a given speed or rate. 

  • Indicating occurrence in an instant of time or a period of time relatively short in context or from the speaker's perspective. 

  • In the direction of (often in an unfocused or uncaring manner). 

noun
  • The at sign (@). 

by

prep
  • Indicates a means of achieving something: Involving/using the means of. 

  • Following a passive verb. 

  • Acted on in units of the specified size or measure. (Sometimes hyperbolically) 

  • Designates a horse's male parent (sire); cf. out of. 

  • Indicates the amount of change, difference or discrepancy 

  • Indicates a means of classification or organisation. 

  • At, with, among 

  • Indicates the creator of a work: Existing through the authorship etc. of. 

  • Not later than (the given time); not later than the end of (the given time interval). 

  • Near or next to. 

  • Following a noun. 

  • Following an adjective. 

  • In the formulae X by X and by Xs, indicates a steady progression, one X after another. 

  • Indicates an authority according to which something is done. 

  • per; with or in proportion to each. 

  • Indicates a referenced source: According to. 

  • Invokes an authority in an oath. 

  • Used to separate dimensions when describing the size of something. 

  • From one side of something to the other, passing close by; past. 

adv
  • Along a path which runs past the speaker. 

  • Aside, away. 

  • To or at a place, as a residence or place of business. 

  • In the vicinity, near. 

adj
  • Out of the way, off to one side. 

  • Subsidiary, incidental. 

How often have the words at and by occurred in a corpus of books? (source: Google Ngram Viewer )