Vestigia quadratorum, cum elevationibus.
_Suppositis iis quæ jam diximus de Contractione optica Quadratorum,
notandum est, vestigium primi Quadrati distare à linea plani spatio ~BA~
opticè contracto; quia linea ~BD~ habet à visuali ~AO~, distantiam ~BA~.
Eodem modo Quadratum secundum distat à linea plani spatio ~EA~, & sic
deinceps._
_Velim observes, in omnibus his Quadratis lineas longitudinis esse partes
visualium, lineas vero latitudinis esse parallelas lineæ plani, & in
primo Quadrato duci ex punctis, in quibus lineæ ~BD~, ~CD~, tendentes ad
punctum distantiæ, secant visualem ~AO~._
_Sub singulis vestigiis Quadratorum, delineavimus alia omnino similia,
per quæ parvo labore fient tres bases, erigendo ad libitum duas primas
perpendiculares æquales; ac ducendo tum duas visuales ad punctum oculi
~O~, tum reliquas, ut in figura. Supponendum est autem, geometricam
altitudinem cujuslibet rei desumi ex lineis normalibus ad lineam plani;
quemadmodum latitudo & longitudo geometrica desumuntur ex eadem linea
plani._
_Tres aliæ bases inferiores formantur sine lineis occultis ex vestigio &
ex elevatione longitudinis opticè deformatis, adhibendo solas altitudines
ac latitudines angulorum. Nomine altitudinis intelligimus distantiam
cujuslibet anguli à linea plani; nomine latitudinis intelligimus
distantiam anguli ab una aliqua linea normali ad lineam plani; dummodo
hæ normales eandem habeant positionem respectu basium, & respectu
vestigiorum & elevationum. Quemadmodum autem per concursum altitudinis
~FG~, & latitudinis ~HI~, ope duorum circinorum invenitur unus angulus in
una basi; ita inveniuntur cæteri tum in ea, tum in reliquis._
The Fifth Figure.
_Plans of Squares, with their Elevations._
Besides what has been already said of the fore-short’ning of Squares in
Perspective, it is convenient to observe, That the Foot of the first
Square is here set within the Line of the Plan, as much as the Space BA
optically contracted; because the Line BD has the Distance BA from the
Visual AO: And in like manner, the second Square is distant from the Line
of the Plan the Space EA; and so for the rest.
I would have you observe in all these Squares, That by the _Length_ I
always understand part of the visual Lines, and by the _Breadth_ those
parallel to the Ground-line; which in the first Square are drawn from
the Points in which the Lines BD, CD, tending to the Point of Distance,
intersect the Visual AO.
Under the Plans of these Squares are described three others just like
them, which are easily converted into three Bases, by erecting, at
pleasure, the two first Perpendiculars of equal Height, and thence
drawing two Visuals to the Point of Sight O, which also bound the rest,
as in the Figure. Observe also, That the Geometrical Height of every
thing is to be set perpendicularly from the Ground-line, or Line of the
Plan, as the Geometrical Length and Breadth are also placed on the same
Line.
The three other Bases below are form’d without the Help of Occult Lines,
by making use only of the Heights and Breadths of the Angles, taken
from the Perspective Plan and Upright. By _Height_ I understand the
Distance of each Angle, or Corner, from the Ground-Line; By _Breadth_,
the Distance of an Angle, or Corner, from any Line perpendicular to the
Ground-line; provided these Lines have always the same Place in respect
of the Bases, as they have in respect of the Perspective Plan and
Upright. And as, by the Help of two Compasses, the Height FG, and the
Breadth HI determine the Corner of the first Base; so, in like manner,
are found the Corners of the other Bases.
[Illustration: FIG. VI.]