I am trying to understand triangulation, especially I am focused on the triangulation Méchain and Delambre achieved in the end of the 18th century, in order to measure the distance between Dunkirk and Barcelona.
I've seen that only one distance has been measured in their whole work, it corresponds to the basis. It is also said that measurement errors have been tracked, by making sure the network of triangles matches.
If I understand this method to track errors correctly, they:
First drew $D_1$ (a first version of $D$) by calculating the length $CD$ (measuring $\hat{A}$, $\hat{D}$) and drawing the intersection between the line $(CM)$ and the circle of radius $CD$.
Then drew $D_2$ (a second version of $D$) by using a protractor at $A$ (they'd have previously measured $\angle DAM$) and stopping by at $D$ thanks to the length $AD$ (calculated using $\hat D$, $\angle DAM$ and $AM$).
Made sure $D_1$ and $D_2$ were very close each one another.
I think my three steps are ok, but I am self-doubting what's in each bullet, because bullet $1$ and bullet $2$ both use the measure of $\hat D$ (measured in the field).
PS:
$D_1$ is a first drawing of the point $D$, it is based on the position of $M$ (which is found based on the basis $AC$, $\alpha$ and $\hat{C}$, by intersecting the circles of radius $CM$ and $AM$) and by taking the intersection of the circle of radius $CD$ and the extension of $(CM)$.
$D_2$ is a second drawing of the point $D$, we here use the measure of the angle $\angle DAM$ (recall $D$ is the place where they decided to stand) and that of $\hat{D}$ and $AM$.
