I shall not expatiate on these Particulars, but leave them for the Exercise of those that are desirous to be informed in Optical Matters, which I am bold to say are comprehended in these three Rules, as fully as the most Inquisitive can desire them, and in all possible Cases; regard being had to the Signs + and -, as in the former Cases of finding the _Focus_. I shall only shew two considerable Uses of them; the one to find the distance whereat an Object being plac'd, shall by a given _Lens_ be represented in a _Species_ as large as the Object it self, which may be of singular Use in drawing Faces and other things in their true Magnitude, by transmitting the _Species_ by a Glass into a dark Room, which will not only give the true Figure and Shades, but even the Colours themselves, almost as vivid as the Life. In this Case _d_ is equal to _f_, and substituting _d_ for _f_ in the Equation, we shall have _pdrρ_ = _ddr + ddρ - dpρr_, and dividing all by _dprρ_ = _dr + dρ - prρ_, that is, _2prρ_/(_r + ρ_) = _d_; but if the two Convexities be of the same Sphere so as _r_ = ρ, then will the distance be = _pr_; that is, if the _Lens_ be Glass = _2r_, so that if an Object be placed at the Diameter of the Sphere distant, in this Case the _Focus_ will be as far within as the Object is without, and the _Species_ represented thereby will be as big as the Life; but if it were a _Plano-Convex_, the same distance will be = _2pr_, or in Glass to four times the _Radius_ of the Convexity; but of this Method I may entertain the Curious at some other Time, and shew how to magnifie or diminish an Object in any proportion assign'd, (which yet will be obvious enough from what is here deliver'd) as likewise how to erect the Object which in this Method is represented inverted. A Second Use is to find what Convexity or Concavity is required, to make a vastly distant Object be represented at a given _Focus_, after the one Surface of the _Lens_ is formed; which is but a Corollary of our Theorem for finding ρ, having _p_, _d_, _r_ and _f_ given; for _d_ being infinite, that Rule becomes _rf_/(_pr - f_) = ρ, that is in Glass _rf_/(_2r - f_) = ρ, whence if _f_ be greater than _2r_, ρ becomes Negative, and _rf_/(_f - 2r_) is the _Radius_ of the Concave sought.