S I M 



and rather buthy at the extremity. It is a native of Guiana, 

 and is a lively, aftive fpecies, and gentle in a Itatc of con- 

 finement. This is the Marikina of Buffon. 



Midas ; Tamarin. This fpecies is taillefs ; beardlcfs ; 

 the upper lip is cleft ; the ears are fquare and naked ; the 

 nails are fubiilate. The tamarin, or great-eared monkey, 

 is about the iize of a fquirrcl ; it is coal-black, except on 

 the lower part of the back, which is of a reddifli colour, 

 and on the hands and feet, which are orange-coloured ; the 

 face is naked and flefh-coloured ; the ears are very large, 

 naked, of a fquarifh form, and of a duflcy flefli-colour ; the 

 tail is very long and black. It inhabits tlie hotter parts of 

 South America. The claws are fnuU and fliarp. It 

 fometimes varies in having the face black, inftead of flefh- 

 coloured. 



SiMiA Marina, the Sea-Ape, in Ichthyology, a name ufed 

 by Bellonius, and fome other authors, for the fifh called 

 "uulpes marina, a kind of fhark, remarkable for its long tail, 

 from which probably it had both one and the other of thefe 

 names. See Sea-Yox. 



SIMICON, in Antiquity, an ancient mufical inftrument 

 of the itringed kind, with thirty-five firings. Mem. de 

 I'Acad. Infcript. vol. v. p. i68. 



SIMICUS, m Biography, an ancient Greek mufician, 

 faid to have been a great improver of mufic. He lived after 

 Homer, and has the reputation of having invented the in- 

 ftrument above-mentioned ; but Plutarch fays, that the 

 ancient Fables attribute this inllrument to Pytocliclus. He 

 alfo informs us, that the Argians fined the firft perfon that 

 ufed it ; but does not tell us how it was ufed, or whether 

 there was a complete fcale for every one of the genera : 35 

 notes in the diatonic fcale would mount it above the addi- 

 tional compafs of modern piano fortes. 



According to Pliny, Simicus added an eighth itring to 

 the lyre of Mercury. Boethius fays that it was Lychaon 

 of Samos ; but Nichomachus gives it to Pythagoras. So 

 many claimants to the fame inventions dellroy all evidence 

 to whom they belong. 



SIMILAR, in Arithmetic and Geometry, the fame with 

 lite. 



Thofe things are faid to be fimilar, or like, which can- 

 not be diftinguidied but by their comprefence ; that is, 

 either by immediately applying the one to the other, or 

 fome other third to them both. So that there is nothing 

 found in one of the fimilar things, but is equally found in 

 the other. 



Thus, if you note all the things in A, which may be 

 difcerned and conceived, without afluming any other ; and, 

 in like manner, note all the things in B, which may be thus 

 conceived, and A be fimilar to B ; all things in A will be 

 the fame with thofe in B. 



Since a quantity cannot be underftood otherwife, than 

 by afluming (ome other quantity to which it may be re- 

 ferred ; fimilar things, notwithltanding their fimilitude, may 

 differ in quantity : and fince, in fimilar things, there is no- 

 thing in which they differ, befide the quantity ; quantity 

 itfelf is the internal difference of fimilar things. 



In mathematics, fimilar parts, as A, a, have the fame 

 ratio to their wholes B, b ; and if the wholes have the fame 

 ratio to the parts, the parts are fimilar. Similar parts A, a, 

 are to each other as their wholes B, b. See Pakt. 



Similar Angles are alfo equal angles. See Solid Angle. 

 Similar ReSangles are thofe which have their lides about 

 the angles proportional. 



Hence, i", all fquarcs mufl be fimilar reftangles. 2°. All 

 fimilar reftangles are to each other as the fquare* of their 

 homologous fides. 



SIM 



Similar Triangles are fuch as have all their three angles 

 refpeftively equal to each other, and the fides about the 

 equal angles proportional. See T riangle. 



Hence, 1°, fince in all triangles mutually equiangular, 

 the corrcfponding fides containing the equal angles are pro- 

 portional, equiangular triangles are fimilar to each other. 

 And if two triangles have their fides refpeftively propor- 

 tional, thofe triangles are equiangular. 



2°. AH fimilar triangles are to each other, as the fquares 

 of their homologous fides. 



In fimilar triangles, and parallelograms, the altitudes are 

 proportional to the homologous fides, and the bafes are cut 

 proportionably by thofe fides. 



Similar Polygons are thofe whofe angles are feverally 

 equal, and the fides about thofe angles proportional. 

 And the like of other fimilar reftilinear figures. 

 Hence, all fimilar polygons are, to each other, as the 

 fquares of the homologous fides. 



In all fimilar figures, the homologous angles are equal, 

 and the homologous fides proportional. All regular figures, 

 and fimilar irregular ones, are in a duplicate ratio of their 

 homologous fides. Circles, and fimilar figures, infcribed in 

 them, are, to each other, as the fquares of the diameters. 

 Similar Arches. See Arch. 



Similar Curves, in Geometry. The fimilarity of curvi- 

 linear figures may be derived from that of reftihnear figures, 

 that are always fimilarly defcribed in them ; or, we may 

 comprehend all forts of fimilar figures, planes, or fohds, in 

 this general definition. Figures are fimilar, when they may 

 be fuppofed to be placed in fuch a manner, that any right 

 line being drawn from any determined point to the terms 

 that bound them, the parts of the right line, intercepted 

 betwixt that point and thofe terms, are always in one con- 

 itant ratio to each other. 



Thus the figures ASD, aS</ (Pto XIII. Geometry, 

 Jig. 14.) are fimilar, when any line S P being drawn always 

 from the fame point S, meeting AD in P, and ad \n p, 

 the ratio of S P to S^ is invariable. It is manifeft, that 

 the reftilinear infcribed figures, apdS, A P D 3, are 

 fimilar in this cafe, according to the definition of fuch 

 figures given in Euclid's Elements, book vi. See Mac- 

 laurin's Fluxions, art. 122. 



When the fimilar figures are in the fituation here de- 

 fcribed, tlicy are alfo fimilarly fituated, and all their ho- 

 mologous lines are either placed upon one another, or 

 parallel. 



Similar Segments of Circles are fuch as contain equal 

 angles. See Segment. 



Similar Conic Sedions are thofe where the ordinates to 

 a diameter in one are proportional to the correfpondent 

 ordinates to the fimilar diameter in the other ; and where the 

 parts of fimilar diameters between the vertices and ordinates 

 in each feftion are fimilar. 



The fame definition alfo agrees to fimilar fegments of 

 conic feftions. 



Similar Diameters of two Conic Sedions. When the dia- 

 meters in two conic feftions make the fame angles with their 

 ordinates, they are fometimes faid to be fimilar. 

 Similar Solids. Sec Like Solid Figures. 

 Similar Bodies, in Natural Philofophy, Inch as have their 

 particles of the fame kind or nature one with another. 



Similar Plain Numbers are thofe which may be ranged 

 into fimilar rcftangles, ;. c. into reftangles whofe fides are 

 proportional; as 6 multiplied by 2, and 12 by 4, the 

 produft of one of which is 12, and the other 48, are fimilar 

 numbers. 



Similar Solid Numbers are thofC) whofe little cube* may 

 5C 2 be 



