I have divided this Figure into two Parts; In the uppermost you have three Squares in Perspective a little shadow’d, distant one from another, according to their Distribution on the Ground-line. BC is the first Square; EF the second. If you then set the Length of a Square on BC, and draw Lines to the Point of Distance, they will intersect the Visual AO in DD. In like manner, if you set another Length of the said Square on EF, and draw to the Point of Distance, you’ll have the second Square in Perspective. The same you may do in the third, and as many as you have occasion for.
In the second Part you see, that if upon the fore-mention’d Plans the Elevations of Cubes or Pedestals were requir’d, it would suffice to elevate the occult and visible Lines from every Angle of the Plan; and determining the Height of the Face L of the first Cube, the Angles of that Face drawn to the Point of Sight, give the Height of all the others.
You may form the same Cubes without occult Lines, drawing only those that are apparent, as you see in the three Cubes that are finish’d and shadow’d; the Perpendiculars of which are taken with the Compasses from the Angles of the Plan, as is shewn in HI of the upper Figure; and the level Lines are transferr’d from the Angles of the Elevation, as in FG of the same Figure.
FIGURA SEXTA.
Modus delineandi opticè sine lineis occultis.
Desiderans facili methodo figuram hanc exponere, dabo rationem elevandi corpora sine lineis occultis, ut in superiori tetigi; ostendam igitur hic, quomodo quinque cubi adumbrati desumantur ab eorum vestigiis, & elevationibus.
Duas debes facere præparationes, si libeat, in chartis etiam separatis. Prima erit formare geometricè vestigium, & elevationem, ut vides in B & A. Secunda erit distribuere super lineam plani latitudinem vestigii B, puta in NM, & in duabus proximis: Illius longitudo MX ducta ad distantiam D, secat visualem MO in R. Spatium autem obliquatum E utile etiam est aliis duobus quadratis positis super eamdem lineam plani; anguli quorum translati ad distantiam B, totidem angulos dabunt inter visuales NO, MO. Hoc posito, duces perpendicularem ad angulum N, quæ in elevationibus geometricis semper necessaria est, eaque tertia linea est, quam supra dixi. Transfer postea altitudinem A in NF, cum visualibus FO, NO, & invenies altitudinem ST. Hoc pariter de cæteris eveniet.
Sciendum superest quonam modo supradicta præparatione uti possis ad construendos stylobatas adumbratos, & inornatos.
Super aliam igitur chartam dispone situm cum duabus lineis, plani scilicet, & horizontis, una cum puncto oculi O, & perpendiculari V, ejusdem mensuræ cum supradicta præparatione, & faciens uti me fecisse vides. Experire postea circino NF æqualia esse 1, 5, & 2, 6. Metire pariter ST, & invenies æqualia 7 & 3; facies postea lineas planas, & visuales ad punctum oculi, & habebis planum superius cubi in 1, 2, 3, 4. Hoc idem faciendum est de aliis. Uno verbo: anguli vestigiorum dabunt tibi lineas perpendiculares, & anguli elevationis dabunt lineas planas; atque hoc semper erit.