VOL. VI.] PHILOSOPHICAL TRANSACTIONS. 635 



determinations of the places in the axis of the images of points however radiat- 

 ing through each kind of lenses. 



Having dispatched these matters, he touches generally concerning the mak- 

 ing a judgment about the appearances of magnitudes, as to their situation and 

 figure, which follow those sorts of reflection and refraction : afterward he 

 shows more fully what kind of images plain objects yield from such reflections, 

 and how they may be delineated. 



Among these things there are interspersed some considerations about divers 

 incident matters, as about the nature of light, and the causes of different co- 

 lours about the rainbow, or colours appearing in pellucid globes ; about some 

 appearances in the glass prism ; concerning the linea refractaria ; concerning 

 the resolution of problems by appropriate lines ; concerning the properties of 

 the conical sections in the reflection of lucid rays, &c. . 



II. Lectiones 13 Geometricae, in quibus (prsesertim) Generalia Linearum 

 Curvarum Symptomata declarantur ab eodem Isaaco Barrow, &c. 4to. 



GDncerning the geometrical lectures, arguing greiit depth in the mathema- 

 tical learning. 



In the first, in order to what follows concerning the generation of magni- 

 tudes, the author treats about the nature of time, as it may be considered in 

 mathematical suppositions about such generations. 



In the second are declared the mathematical hypotheses about simple mo- 

 tions, progressive and circular, which serve to the production of magnitudes, 

 with some general remarks on the natures, dimensions, and properties (con- 

 sequent on such productions) of magnitudes. There is also a touch about the 

 method of indivisibles, explaining how in some cases it is to be understood 

 and applied. 



The third treats about the generation of magnitudes by the composition and 

 concourse of motions. 



In the fourth and fifth, from one generation propounded of curve lines, 

 supposing them produced by two motions, one uniform, the other accelerated, 

 divers theorems are inferred, implying so many general properties of curve 

 lines. 



The next five lectures contain many theorems, and problems about readily 

 determining the tangents of curve lines, immediately by them, without other 

 computation ; particularly, there are divers single theorems, whereby the tan- 

 gents of all curves commonly known or considered in geometry, the conical 

 sections, conchoids, cissoids, spirals, quadratrices, &c. are determined in ways 

 so general, as to comprehend also the like determination of tangents in regard 

 to innumerable other curves, generated in a common manner with them. Of 



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