POLYGAMY 



4745 



POLYGON 



Minor. For a time his good fortune was so 

 uninterrupted that he was called the "darling 

 of the gods," but his exceeding prosperity 

 helped to bring about his downfall. Herodotus 

 tells that the Egyptian king Amasis, a strong 

 ally of Polycrates, became alarmed lest the 

 gods, in jealousy, should turn against the 

 Samian despot; and he implored Polycrates to 

 sacrifice to them some possession which he 

 valued highly. Accordingly, Polycrates threw 

 into the sea a ring of great worth, which the 

 next day was found in the belly of a fish 

 that had been presented to him. Looking up- 

 on this as a sign that the gods would not 

 accept the sacrifice, Amasis broke the alliance. 

 About 522 B.C. a Persian ruler of Sardis in- 



1 Polycrates to visit him, and on his ar- 

 rival had him put to death. 



POLYGAMY, polig'ami, a system of mar- 

 riage by which a man has more than one 

 wife at one time. The word, commonly used 

 in this sense, is from two Greek words mean- 

 ing many marriages, and in its widest sense 

 includes polyandry also, which is the term for 

 many husbands; but polygamy is the more ac- 

 curate term used to denote a plurality of wives. 

 From earliest times to the present the taking 

 of more than one wife has been common among 

 various races, though never in the world's his- 

 tory has it been the only form of the marriage 

 relation. It was not forbidden among the an- 

 cient Greeks, but was very seldom practiced, 

 and it gained almost no hold among the Ro- 

 mans. The Britons practiced it, but it was 

 very rare among the early Germans, a fact 

 which the Roman historian Tacitus finds 

 worthy of note. 

 In Oriental countries polygamy is often per- 



d, and sometimes enjoined, by the religion 

 of the state. Mohammedans may have four 



*, but among them, as among other peo- 

 ples who approve of polygamy, the custom 



ly obtains only among the wealthy classes, 

 h< poor man cannot support more than 

 one wife, even in tin- primitive style in which 

 he lives. Among th. Hindus there are no 

 restrictions as to number, and a harem of one 

 hundred wives is by no means unknown. Chi- 

 nese law permits of but one v. 



indent Jewi-h law permit tod polygamy, 



/h it was not generally practiced, and the 



Bir>! no injunction against it. Chn>- 



er, ln.> always strongly opposed 



<nd laws against it exist in all Chn-tian 



In tin- I'nited States the Mormons, 



enj. i-nto by their religion, practi<l 



polygamy openly until 1890, when Congress 

 passed laws absolutely forbidding plural mar- 

 riages. . E.D.F. 



POLYGON , pol ' i gon. A plane figure bounded 

 by three or more straight lines is called a 

 polygon. The bounding lines are called the 

 sides; the sum of the sides is the perimeter. 

 The angles formed by the sides are the angle* 

 of the polygon, and the meeting points of the 

 sides are the vertices of the polygon. A poly- 

 gon is a triangle, quadrilateral, pentagon, hexa- 

 gon, heptagon, octagon, etc., according as the 

 sides number three, four, five, six, seven, eight, 

 etc. If all the sides are equal, the polygon is 

 equilateral. If all the interior angles are equal, 

 the polygon is equiangular. 

 . The angles in- 

 side the perim- 

 eter r,re called 

 the i.iterior an- 

 gles. If the sides 

 are extended they / 

 form other angles 

 lying outside the 

 polygon, which 

 are called the ex- 

 terior angles. 



In Fig. 1 the 

 angle a b c is an interior angle ; the angle h b c 

 is an exterior angle. 



The sum of the interior angles of a triangle 

 is 180, or two right angles. The sum of the 

 interior angles of a quadrilateral is 360 or four 

 right angles. The sum of the interior angles 

 of any polygon is the number of sides minus 

 t, times two right angles. This can be seen 

 by dividing any polygon into triangles, as in 

 Fig. 1. There are as many triangles as sides 

 of the polygon; the sum of the angles of 

 each triangle is two right angles. The sura of 

 the angles at the center is four right angles. 

 So the sum of the interior angles of the poly- 

 gon equals six times two right angles, minus 

 the four right angles at the ccntrr. or sum of 

 tior angles: this may be stated 6X2 right 

 angles 2X2 right angles, or (6 2)X2 right 

 angles. 



Let n stand for tin- number of sides of any 

 polygon and * for tin- number of degrees in the 

 sum of its int< !< s. and we have: 



=(n 2) X2 rt. angles 



or 



=<n-2)Xl80* 



>um of the exterior angles of a polygon, 

 ng one at each vertex, is four right angles, 

 or 360. 



