. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. 124 SURVEYING. PROBLEM I. To divide a triangle into two parts, having a given ratio of m to n. Case 1. By a line drawn from one angleto its opposite side. Let ABC represent the triangle; divideits base into two parts, corresponding to thegiven ratio, and let AD be one of the parts;then we shall have the following proportion. AD : AB : : m : m-\-n m n Whence, AD=-^AB) and BD=—{AB) Now the two parts are numerically known, and are to each other asm to n. Triangles, hav
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. 124 SURVEYING. PROBLEM I. To divide a triangle into two parts, having a given ratio of m to n. Case 1. By a line drawn from one angleto its opposite side. Let ABC represent the triangle; divideits base into two parts, corresponding to thegiven ratio, and let AD be one of the parts;then we shall have the following proportion. AD : AB : : m : m-\-n m n Whence, AD=-^AB) and BD=—{AB) Now the two parts are numerically known, and are to each other asm to n. Triangles, having the the same altitudes, are to oneanother as their bases. Therefore, ADC : CDB : : m : n as re-quired. Case 2. By a line parallel to one of itssides. Let DE divide the triangle as required,and as similar triangles are to one anotheras the squares of their homologous sides,therefore: (AB)2 : (AD)2 : : m-\-n : n Whence, AD^AB*/ m m-\-n Which shows that if we have the numerical value of AB, and ofn and m, we can find that of AD, and from D draw DE parallelto BO, and the triangle is divided as required. Case 3. By a line
Size: 1735px × 1439px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., boo, bookcentury1800, booksubjectnavigation, booksubjectsurveying
