Why are first and third angle projections so named?

The terms first angle projection and third angle projection may seem like complicated terms but the reason for their naming is connected with geometry. Figure 2.15 shows four angles given by the planes OA, OB, OC and OD. When a part is placed in any of the four quadrants, its outline can be projected onto any of the vertical or horizontal planes. These projections are produced by viewing the parts either from the right-hand side or from above as shown by the arrows in the diagram. In first angle projection the arrows project the shape of the parts onto the planes OA and OB. When the two planes are opened up to 180 ~ as shown in the small diagrams in Figure 2.15, the two views will be in first angle projection arrangement. When the part in the third quadrant is viewed from the righthand side and from above, the view will be projected forwards onto the faces OC and OD. When the planes are opened up to 180 ~ the views will be in third angle projection arrangement, as shown in thesmall diagrams in Figure 2.15. If parts were to be placed in the second and fourth quadrant, the views projected onto the faces when opened out would be incoherent and invalid because they cannot be projected from one another. It is for this reason that there is no such thing as second angle projection or fourth angle projection. There are several ISO standards dealing with views in first and third angle projection. These standards are" ISO 128"1982, ISO 128-30:2001 and ISO 128-34:2001. 
Engineering Drawing for Manufacture
by Brian Griffiths
Publisher: Elsevier Science & Technology Books