SIMILAR, in arithmetic and geometry, the same with like. Those things are said to be similar, or like, which cannot be distinguished but by their compre. sence, that is, either by immediately ap plying the one to the other, or some other third to them both, so that there is nothing found in one of the similar things but is equally found in the other, not withstanding their similitude may differ in quantity ; and since, in similar things, there is nothing wherein they differ be sides the quantity : quantity itself is the internal difference of similar things. In mathematics, similar parts have the same ratio to their wholes, and if the wholes have the same ratio to the parts, the parts are similar. See PART.
Similar angles are also equal angles. In solid angles, when the planes under which they are contained are equal, both in number and magnitude, and are dis posed in the same order, they are similar, and consequently equal. Similar arches of a circle are such as are like parts of their whole circumferences, and conse quently equal. Similar plane numbers are those numbers which may he ranged into the form of similar rectangles, that is, into rectangles whose sides are pro portional; such are 12 and 48; for the sides of 12 are 6 and 2, and the aides of 48 are 12 and 4: but 6 : 2 : : 12 : 4, and therefore those numbers are similar. Si milar polygons are such as have their an gles severally equal, and the sides about those angles proportional. Similar rec
tangles as those which have their sides about the equal angles proportional : hence, 1. All squares are similar rectan gles. 2. All similar rectangles are to each other as the squares of their homo logous sides. Similar right-lined figures are such as have equal angles, and the sides about those equal angles propor tional. Similar segments of a circle are such as contain equal angles. Similar curves : two segments of two curves are called similar, if any right-lined figure being inscribed within one of them, we can inscribe always a similar right-lined figure in the other. Similar conic sec tions: two conic sections are said to be similar, when, any segment being taken in the one, we can assign always a simi lar segment in the other. Similar dia meters of two conic sections : the dia meters in two conic sections are said to be similar, when they make the same an gles with their ordinates. Similar solids are such as are contained tinder equal numbers of similar planes, alike situated. Similar triangles are such as have their three angles respectively equal to one another : hence, 1. All similar triangles have the sides about their angles propor tional. 2. All similar triangles are to one another as the squares of their homolo gous sides.