The sole purpose of these instruments was to multiply objects by reflexion; and so little did the idea of producing a symmetrical picture enter into Baptista Porta’s contemplation, that he directs the mirrors to be placed at any angle, because the multiplying property of the mirrors is equally developed, whatever be the angle of their inclination.
The show-box of which Porta speaks with such admiration, has so many mirrors, and these are placed at such angles, that not one of the effects of the Kaleidoscope can be produced from them. Its beauty is entirely derived from the accumulation of individual images.
The next competitor for the invention of the Kaleidoscope is the celebrated Kircher, who describes, as an invention of his own, the construction of two mirrors which can be opened and shut like the leaves of a book. This instrument is represented in [Fig. 54], and is described in the following passage:—
Fig. 54.
Parastasis I.
Specula plana multiplicativa sunt specierum unius rei.
Vide Fig. 54.
Mira quædam et a nemine, quod sciam observata proprietas elucescit in duobus speculis ita constructis, ut ad instar libri claudi et aperiri possint; ponantur illa in plano quopiam, in quo semicirculum in gradus suos descriptum habeas. Si enim punctum, in quo specula committuntur, in centro semicirculi statuas, ita ut utrumque speculi latus diametro insistat, semel tantam videbitur rei imago, apparebuntque duæ res, una extra speculum vera, altera intra, phantastica: Si vero specula ita posueris, ut divaricatio laterum 120 gradus intercipiat, videbis rei intra latera est, quia angulus reflexionis et incidentiæ tantus est, quantus est angulus interceptus a lateribus, videlicet 120 grad. qui cum obtusius sit, non nisi binam imaginem causare potest, ut in Propos. v. fol. 848, ostensum est. Si vero specula interceperint angulum 90 graduum, videbis in plano circulum in quatuor partes divisum, in quibus totidem simulacra rei positæ comparabunt, tria phantastica, et unum verum; cum enim reflectio fiat ad angulos rectos utrumque latus reflectens formam causabit intra se alias duas formas, unde et consequentur pro multiplicatione laterum formæ multiplicabuntur, quæ et in reflectione laterum normam servabunt uti in Propos. v. fol. 848, ostendimus. Porro si speculorum latera interceperint angulum 72 graduum, videbis in plano horizontali efformari perfectum et regulare pentagonum, in quo totidem formæ apparebunt, item, si sexaginta graduum interceperint angulum, videbis hexagonum totidemque formas quinque nimirum phantasticas unam veram. Ita, si speculorum angulus interceperit 51 gradus cum ³/₇ comparebit perfectum heptagonum, cum totidem rei intra specula collocatæ formis; non secus angulus speculorum 45 graduum dabit octogonum; 40 graduum dabit enneagonum; 36 graduum decagonum; 32 graduum angulus cum ⁸/₁₁ dabit endecagonum et denique angulus 30 graduum referet dodecagonum cum totidem formis, et sic in infinitum; ita ut semper tot laterum sit futurum polygonum anacampticum totidemque formarum, quot polygonum cuivis latus speculorum intercipit divaricatio, latera habuerit: quorum omnium rationes dependent a Propos. v. precedentis distinctionis. —Kircheri, Ars Magna Lucis et Umbræ. Rom. 1646, p. 890.