We introduce MosAIc, an interactive website that allows users to discover hidden connections between works of art across culture, media, artists, and time. MosAIc finds "visual analogies", or works of art with the same semantic structure but very different cultural and artistic context, within the combined works of the Metropolitan Museum of Art and the Rijksmuseum. Users can take any work from the collection and find analogous works in particular genres, cultures, or media of art. Our approach finds visual analogies that mirror larger scale cultural trends, such as the flows of artistic techniques across the globe due to trade routes. Our approach is based on generalizing deep image retrieval methods to flexibly adapt to logical filters and predicates. This allows image retrieval methods to find close matches in different regions of the image collection, an approach we call "Conditional Image Retrieval".