VOL. v.] ' rniLOSOPHlCAL TRANSACTIONS. 563 



II. Physica, in decern Tractatus Disthbuta, Auth. Honorato Fabri, S.J. Lug- 

 duni Galliarum, 1669, in 4to. 



Of this vast work the author published, An. 1666, at Paris, two treatises; the 

 first, De Piantis et Generatione Animalium: the latter, De Hoinine; by a kind 

 of retrograde method opposing the order of publishing to that of composing; 

 for, whereas in the composition, he proceeded from the simpler things to the 

 more complex, in the publication and communication, he thought fit to produce 

 the sum of all nature, that elaborate piece, man; in whom, besides the sensi- 

 tive and vegetable faculties, and the powers of mixts and the elements common 

 to all bodies, there shines out a supereminent principle, the rational soul. In 

 the preface the author gives an account of the method used by him in this whole 

 work, and of his performance in this very volume. 



END OP VOLUME FIFTH OP THE OfilGINAL. 



A Solution, given hy Mr. John Collins, of a Chorographical Problem, 

 proposed hy Richard Totfnley, Esq. N" 69, p. 2093. Fol. FI, 



Problem. The distances of three objects in the same plain, being given, as 

 A,B,C; the angles made at a fourth place in the same plain, as at S, are ob- 

 served. The distances from the place of observation to the respective objects are 

 required. 



The problem has six cases. See pi. 13, fig. 10, 11, 12, 13, 14, 15. 



Case I. — If the station be taken without the triangle made by the objects, 

 but in one of the sides thereof produced, as at S, in fig. 10, find the angle ACB; 

 then, in the triangle ACS, all the angles and the side AC are known, whence 

 either or both the distances SA or SC may be found. 



Case II. — ^If the station be in one of the sides of the triangle, as at S, in fig. 

 II, then having the three sides AC, CB, BA, given, find the angle CAB; 

 then again in the triangle SAB, all the angles, and the side AB are known, 

 whence may be found either AS or SB, geometrically, if you make the angle 

 CAD equal to the observed angle CSB, and draw BS parallel to DA, you de- 

 termine the point of station S. 



Case III. — If the three objects lie in a right line, as ACB, fig. 12, suppose it 

 done, and that a circle passes through the station S, and the two exterior ob- 

 jects A, B ; then is the angle ABD equal to the observed angle ASC (by 21 of 

 the 3d book of Euclid) insisting on the same arch AD; and the angle BAD in 

 like manner equal to the observed angle BSC; by this means the point D is de- 



4b2 



