156 Mohs’s &yste7n of C^ydallography 
and the edges of combination niadd by its faces with each other 
are parallel^ as in Fig. 4. JPL Vlll. 
9* Statement qf the foregoing problem^ for a combination 
(f two rhomboids, — I’his parallelism evidently arises from the 
dimensions of the rhotoboids, in othet words, from the magni- 
tude of their angles, because it disappears whenever the di- 
mensions of the one or the other are changed. The foregoing 
problem, (4. 5.) therefore requires, to find the ratio of the di- 
mensions by which the edges qf combination are rendered parallel, 
lOi Solution, Upright position, — Place a rhomboid in 
such a position, that the straight line passing through two cor- 
ners (solid angles,) formed by equal plane angles, may be ver- 
tical. Those corners are named the summits^ that line the axis. 
In this position the rhomboid stands upright. Rhomboids, 
therefore, stand upright, when their axes are perpendicular. 
Hi Horizontal projection, — From those solid angles of a 
rhomboid^ which are not summits^ let fall perpendiculars upon 
a horizontal plane, and connect the points where they meet the 
plane by straight lines. The figure which results will be a 
regular hexagon ; it is called the horizontal projection of the 
rhomboid i 
12. Derivation qf a more obtuse rhomboid.--^'EYmg a rhom- 
boid into the upright position ; and through those edges which 
meet in the extremity of the axis, stretch planes equally inclined 
to the faces of the rhomboid. Extend these planes till they all 
intersect each Other : the solid bounded by them will in its turn 
be a rhomboid, Figs. 2. & 3. PL VIII., Fig. 2. the original, 
Figi B. the derived with the original. 
13. The horizontal projection qf this four times that of the 
preceding,'^--^\iQ axis of this new rhomboid is equal to that of 
the preceding, (Fig. 3. PL VIII.) The horizontal projection 
is equal in area to four times, in periphery to twice, the horizon- 
tal projection of the latter. 
14. Together, they produce parallel edges qf combination , — 
This new rhomboid has a position different from that of the 
first (7). The edges of the former have a similar situation with 
the oblique diagonals of the latter ; that is to say, they lie in 
the same vertical plane with those diagonals. If sections are 
drawn parallel to the faces of the new rhomboid, and lying 
