A manual of the principles and practice of road-making: comprising the location, construction, and improvement of roads, (common, macadam, paved, plank, etc.) and rail-roads. By W. M. Gillespie ...

APPENDIX C. 401
Substituting A o in the above;
AF = /[2FP(AF + F i) tan. ~ - - pr-].
AF2 =2FP, AFtan. I + 2FP, Ftan. I - rPI
AFP2 - 2F P,tan. ~ I, A F= 2F P, tan. I - p2.
AF =F P, tan.,I ~ \/(2 F p, FI tan. i - FPp2 +F p2 tan.2 I)
A F = F P, tan. i I ~:/[(F P, tan. i I + i)2 - F I2- F P2].
Note to Case A, Probs. i, 11, IIZ., and IFV
When the intersection, I, of the tangents is inaccessible, D~ and
t must be calculated. Fig. 5. From A, run one or more lines to meet
the other tangent at some point, as w. Then the desired angle
at I is obtained by subtracting the sum of all the interior angles
Fig. 5.
A~ s \
from two right angles, taken as many times, less two, as the figure
has sides. When the lines are run by traversing, the reading from
w to z at once gives D~. A w is calculated by latitudes and departures. Then IA, in the triangle AI w is calculated by trigonometry.