Ex elevatione geometrica A eruitur vestigium B. Hoc autem deformato in C & D, ex circulis vestigii C habentur latitudines columnæ, quadræ, ac tori triplicis basis: & eodem modo ex vestigio D habentur latitudines quadræ ac tori ultimæ basis. Ex maximis latitudinibus circulorum vestigii C ereximus perpendiculares ad partes quæ ipsis respondent in basi; ut agnoscas quænam sint puncta maximæ latitudinis in eisdem partibus. Hæc puncta (quæ in circulo maximo vestigii C sunt M & N) invenientur tangendo circumferentiam uniuscujusque circuli regulâ parallelâ ad lineam perpendicularem E, nam si figura exactè delineata fuerit, regula tanget singulos toros trium basium in punctis maximæ hinc inde latitudinis.
Magis laborandum erit in reperiendis altitudinibus quatuor basium. Verum si sedulò inspiciatur deformatio elevationis F, aliarumque duarum, (quæ factæ sunt, notatis in linea perpendiculari E divisionibus desumptis ex elevatione geometrica A) constabit, nullum esse punctum in circulis vestigii C, cui nequeat inveniri punctum correspondens in toro & quadra ipsius basis, ut ostendunt lineæ occultæ, quæ incipiunt ex M & N. Earum quælibet ex vestigio C pervenit ad lineam visualem, & continuatur cum linea altitudinis ex visuali ad elevationem F, & cum alia linea latitudinis ex elevatione F ad basim. Porrò ex figura constat, superficiem superiorem quadræ subduci oculis à columna, & aliquid ex parte postica tori quod cæteroqui conspiceretur, abscondi à quadra. Proinde torus, qui ex punctis maximæ latitudinis retrorsum flectitur, eousque delineandus est, quoad hinc inde occurrat quadræ ipsum cooperienti. Præstaret autem singula membra ita exactè delineari, quasi essent diaphana; ut partes oculis imperviæ, omnino cohæreant cum partibus quæ ipsis conspicuæ sunt.
Completâ delineatione, si figuram tuam ex perpendiculo puncti oculi ex debita distantia contemplatus fueris, omnes defectus facilè deteges & statim corriges. Præcipuam diligentiam pones in formando & emendando toro, qui habet duas rotunditates; unam quatenus ambit columnam; alteram quatenus caret angulis, ut ostendit elevatio geometrica in I.
The Sixteenth Figure.
The Tuscan Base in Perspective.
From the Geometrical Elevation A, is drawn the Plan B; which being put into Perspective, as you see in C and D, from the Circles of the Plan C you have the Breadths of the Column, and of the List, and Torus of the three Bases: And after the same manner, by the Plan D, you have the Breadth of the List and Torus of the last Base. From the greatest Breadth of the Circles of the Plan C, we have erected Perpendiculars to the Parts that answer them in the Base, to the end that you may see where the Points fall, which terminate the greatest Breadth of those Parts. These Points (which in the biggest Circle of the Plan C are M and N) are found by touching the Extremity of the Circumference with a Line parallel to the Perpendicular E: for if the Figure were exact, that Line would touch every Torus of the three Bases in the extreme Points of their Breadth.
The Heights of the four Bases are something more difficult to be found. Nevertheless, if you consider well the Elevation F, and the other two G and H, (which are made by transporting the Divisions of the Elevation A upon the Perpendicular E) it will plainly appear that there is no Point in the Circles of the Plan C, to which there may not be a correspondent Point found in the Torus and List of the said Base; as the occult Lines shew, that arise from M and N; each of which is a Continuation of three Lines: The first of Breadth, from the Plan C to the Visual; the second of Height, from the Visual to the Elevation F; the third of Breadth, from the Elevation F to the Base. Now, tho’ it’s plain by the Figure, that the Body of the Column prevents the Sight of good part of the Fillet, and the same Fillet takes off from part of the Torus, which would otherwise be visible; for which Reason the Back-part of the Torus is continu’d only till it meet the same: Yet it’s certainly best to draw every Member complete, as tho’ the Work were transparent; that the Parts hidden from the Eye may the better agree with those that are expos’d to it.
When your Draught is finish’d, if you view it at the due Distance, and perpendicularly to the Point of Sight; you’ll readily discover and rectify what’s amiss. Your chief Care will be employ’d in shaping the Torus, difficult by reason of its Roundness both ways; namely, in the Contour of its Moulding, as in the Elevation I; and in the Circuit it makes about the Column.