The Manner of designing in Perspective without occult Lines.
Being desirous to make this Rule as easy as possible, I shall give a farther Account of raising Solids without the Help of occult Lines, which I only touch’d upon in the foregoing Figure. I therefore here shew you, how the five shadow’d Cubes of this Figure are taken from their Plans and Elevations.
Two things preparatory are to be done, and, if you please, on separate Papers. The first is, to describe the Geometrical Plan and Elevation, as you see in B and A. The second is, to dispose on the Ground-line the Breadth of the Plan B; as, for Example, in NM, and the two next to it. The Length thereof MX, drawn to the Point of Distance D, cuts the Visual MO in R; and the Foreshortning E serves also for the other two Squares plac’d upon the same Ground-line, whole Angles being directed to the Distance D, give as many Angles on the Visuals NO, MO. This done, erect a Perpendicular on the Angle N, which in Geometrical Elevations is always necessary, and is the third Line mention’d in the first Figure. Then carry the Height A on NF, drawing the Visuals FO, NO, which determine the Height ST, and that of the other Squares.
It remains to be known, how to make use of the foresaid Preparation for the Construction of the shadow’d Pedestals.
On another Paper therefore dispose the Horizontal and Ground-lines, together with the Point of Sight O, and the Perpendicular V, keeping the same Measures as in the aforesaid Preparation, and doing as I have done. You may prove by the Compasses, that NF is equal to 1, 5, and 2, 6, and measuring ST, you’ll find it equal to 7, 3, then drawing the level Lines, and the Visuals to the Point of Sight, you have the upper Face of the Cube C in 1, 2, 3, 4. The same must be done in the others. In a word, the Angles of the Plan give you the perpendicular Lines, and the Angles of the Elevation give the level Lines, or those parallel to the Ground-line; and this you are always to understand for the future.
FIGURA SEPTIMA.
Aliud exemplum construendi vestigium geometricum, cum elevatione longitudinis.
Vides hic stylobatam P in quatuor partes divisum, & adumbratum. Si illum opticè delineare velis, construere debes supradictas præparationes, geometricam nempe, & opticam. Nomine geometricæ intelligo vestigium A, & elevationem B; nomine vero opticæ, totum id quod includitur in GCDEO.
Transfer igitur latitudinem geometricam CD vestigii A super lineam plani pariter CD, & transfer longitudinem DE super lineam plani pariter DE, operans more solito; & habebis vestigium opticé. Transfer posteà elevationem HX in CG perpendicularis; ducens visualem GO, eleva ad lineam GO omnem angulum, quem planum facit in linea CO, & habebis altitudinem necessariam etiam sectionis.
Transferes denique circino in aliam chartam angulos vestigii, qui dabunt tibi lineas perpendiculares, & anguli sectionis dabunt lineas planas: Visuales vero duces ad punctum oculi.