Final answer:
The two styles are the Perpendicular style, a phase in English Gothic architecture characterized by vertical lines, and the Rectilinear style, which broadly refers to the use of straight lines in visual art to create structure and perspective.
Step-by-step explanation:
The two styles mentioned in the given content are the Perpendicular style and what seems to be alluded to as the Rectilinear style, which refers to the use of straight lines and right angles in the construction and decoration of buildings, as well as in the creation of perspective in paintings. The Perpendicular style is specifically known as a phase in English Gothic architecture, marked by vertical lines and a grid-like arrangement, which came into prominence after the Black Death, lasting through the later medieval period. In contrast, the concept of rectilinear style can be related to the broader use of straight lines within art and architecture, which can include the use of orthogonals in linear perspective, as well as the classic lines found in sculptures like the Laocoon Group and in the structural elements of paintings such as Velazquez's Las Meninas.
While the Perpendicular style is clearly defined within the context of English Gothic architecture, the term 'Rectilinear style' is not a widely recognized term in art history; it may have been meant to describe the use of straight, horizontal, vertical, and diagonal lines that provide stable structures in visual composition. This use of straight lines is evident across various forms of visual arts, including painting, sculpture, and architecture, often contributing to the illusion of depth and space, as seen in techniques like linear and atmospheric perspective.