At the beginning of the scientific research on vaulted structures, during the eighteenth century, scholars such as De la Hire, Couplet and Coulomb, primarily considered an arch made of voussoirs with the joints that have neither friction nor cohesion between them. Accordingly, in order to ensure the equilibrium of the voussoirs, for given extrados and intrados, the problem of determining the direction of the joints was imposed, since the resultant thrust forces must be perpendicular to them. This paper derives and elaborates in detail the explicit equation that defines the precise position and orientation of the joints in a triangular arch of general shape. For the two commonly used shapes, namely flat arch or plate-bande and triangular arch with its intrados and extrados both perpendicular to springings, the closed-form expression of thrust line is obtained. In addition, the paper provides the minimum thickness for various springing angles.