Page:Philosophical Transactions - Volume 003.djvu/252

 and Earth. The Increase, and Diminution, the Transformation and Comparison of divers Solids, and the Mensuration of divers of their Surfaces.

3. Of Opticks 3 Books.

In the first, he handleth the simple and direct Appearances-of Objects meaning such appearances as are not liable to Reflection or Refraction; and herein he saith, that passing by slight matters, he onely treats of such as are either new, or of the better esteem; such as are the Properties of the sight, the manner of its perceiving a Distance; and the Place of the Eye being assigned, to find that Height, in which a greater Length or Breadth shall appear equall to a lesser Length or Breadth, or any assigned Length or Breath shall appear in a given Proportion. He likewise finds the Portion of a Cone or Cylinder; seen according to the Magnitude of the Figure, and Position of the Eye, and explains the Moons Phases.

In the 2d. He handles the Theory and Practice of the Perspective or Scenographic Projection, or Transcription of a given Magnitude into a Plain, which cuts the Optick Pyramid, wherein he explains the Direct appearance, and the Monstrous defamation of an Object, which at a certain place shall appear beautiful.

In the 3d. He treats of the Astronomick Projections of the Spheare, and thence derives the triple Astrolabe, and shews their uses, and the Conveniences or Inconveniences of each Projection: viz. the Projection on the Plain of the Æquator,  the Eye being in one of the Poles; or on the Plain of the Colure of the Solstices, the Eye being in one of the Æquinoctial Points; and the Orthographick Projection, by Perpendiculars, falling from the respective Points of the Circles of the Spheare, on the Projecting Plain: Such a Projection, if the Plain be the Meridian, Ptolomy called the Analemma.

If the Eye be in the Zenith of Nadir projecting, on the Plain of the Horizon, the Author sheweth, that the Projection will be the same, as if the Eye were in one of the Poles projecting on the Plain of the Æquator, onely the names of Circles are changed.

Pag. 205. Nam Circular qui in illa referebat Æquatorem, in hac Horizontem repræsentat; & Projecturæ Tropicorum reliquorumq; Æquatori parallelorum in illa, in hac sunt Projecturæ parallelorum Horizonti seu Almicantarath: rursum qui in illa sunt Projecturæ Horizontis, Almicantarath & Verticalium, in hac projecturæ erunt Æquatoris & Parallelorum ejus, ac Meridianorum. Postremo rectæ lineæ, quæ per Centrum Projectonis ductæ, erant projecturæ Meridianorum in illa, in hæc erant Verticalium Projecturæ; quare qui illius Projectionis modum prove intellexerit, hanc qucq; nullo negotio perficiet. Rh