APP 



APP 



favour of the court : by guardian and 

 next friend, when underage. 



APPELLATIVE, in grammer, a noun, 

 or name, which is applicable to a whole 

 species or kind, as man, horse ; in contra- 

 distinction to a proper name. 



APPELLOR, or APPELLANT, in law, 

 he who has committed some felony or 

 other crime, which he confesses and ap- 

 peals, that is, accuses his accomplices. 



APPENDANT, in law any thing that 

 is inheritable, belonging to some more 

 worthy inheritance, as an advowson, com- 

 mon, or court, may be appendant to a 

 manor, land to an office, &c. but land 

 cannot be appended to land, for both are 

 corporeal inheritance, and one thing cor- 

 poreal cannot be appendant to another. 



APPLE, a well-known fruit, consisting 

 of a rind, pill, or skin; the pulp, or paren- 

 chyma; the branchery, or seed-vessels ; 

 and the core. See PYHUS. 



APPLICATION, the act of applying 

 one thing to another, by causing them to 

 approach or bringing them nearer toge- 

 ther. Thus a longer line or space is 

 measured by the application of a less, as 

 a foot or yard by an inch, &c. ; and mo- 

 tion is determined by successive applica- 

 tion of any thing to different parts of 

 space. Application is sometimes also 

 used both in arithmetic and geometry, 

 for the operation of division, or for that 

 which corresponds to it in geometry. 

 Thus 20 applied to, or divided by 4, i. e. 

 ^0 

 ^-, gives 5. And a rectangfe a b applied 



to a line c, gives the fourth proportional 



, or another line, as, d, which, with the 

 c 



given line c, will contain a rectangle c d 

 = b. 



APPLICATION, in geometry, denotes the 

 act of placing one figure upon another, 

 in order to determine their equality or 

 inequality. In this way Euclid, and other 

 geometricians, have demonstrated some 

 of the primary and fundamental proposi- 

 tions in elementary geometry. Thus it is 

 proved, that two triangles, having two 

 sides of the one equal respectively to two 

 sides of the other, and the two included 

 angles equal, are equal in all respects ; 

 and two triangles, having one side and the 

 adjacent angles of the one respectively 

 equal to one side and the adjacent angles 

 of the other, are also in the same mode 

 of application shewn to be equal. Thus 

 also is demonstrated, that a diameter di- 

 vides the circle into two equal parts ; and 

 that the diagonal divides a square or pa- 

 rallelogram into two equal parts. The 



term is also used to signify the adapta- 

 tion of one quantity to another, in order 

 to their being compared, the areas of 

 which are the same, but their figures dif- 

 ferent. Thus Euclid shews how, on a right 

 line given, to apply a parallelogram that 

 shall be equal to a right-lined figure given. 

 APPLICATION of one science to another, 

 signifies the use that is made of the prin- 

 ciples of the one for augmenting and per- 

 fecting the other. As there is a connec- 

 tion between all the arts and sciences, one 

 of them may be made subservient to the 

 illustration and improvement of the other; 

 and to this purpose algebra has been ap- 

 plied to geometry, and geometry to alge- 

 bra, and both to mechanics, astronomy, 

 geography, navigation, &c. See ALGE- 

 BRA, application of. 



APPLICATION of algebra qnd geometry to 

 mechanics is founded on the same princi- 

 ples as the application of algebra to geo- 

 metry. It consists principally in respre- 

 senting, by equations, the curves describ- 

 ed by bodies in motion, by determining 

 the equation between the spaces which 

 the bodies describe, when actuated by any 

 force, and the times employed in describ- 

 ing them. As a familiar instance, we may 

 refer to the article ACCELERATION, where 

 the perpendiculars of triangles represent 

 the times, the bases, the velocities, and 

 the areas the spaces described by bodies 

 in motion, a method first invented by Ga- 

 lileo. As lines and figures may be treat- 

 ed of algebraically, it is evident in what 

 way the principles of geometry and al- 

 gebra may be applied to mechanics, and 

 indeed to every branch of mixt mathe- 

 matics. 



APPLICATION of mechanics to geometry, 

 consists in the use that is made of the 

 centre of gravity of figures, for determin- 

 ing the contents of solid bodies described 

 by those figures. 



APPLICATION of geometry and astronomy 

 to geography, consists in determining- the 

 figure and magnitude of the earth ; in de- 

 termining the positions of places by ob- 

 servations of latitudes and longitudes ; 

 and in determining, by geometrical opera- 

 tions, the positions of such places as are 

 not far distant from one another. 



APPLICATION of geometry and algebra to 

 natural philosophy was invented chiefly by- 

 Sir Isaac Newton, and upon this applica- 

 tion are founded all the mixed sciences 

 of mathematical and natural philosophy. 

 Here a single observation or experiment 

 will frequently produce a whole science, 

 or branch of science. Thus, when it is 

 proved by experiment that the rays of 



