VOL. III.] PHILOSOPHICAL TRANSACTIONS. 315 



these, measures such solids as are contained in the mundane bodies, as the 

 surface of the whole earth ; where he is pleased to conclude, that at the day of 

 judgment a less portion of it than England will serve to hold all its inhabitants 

 and their infants, that ever have been, or in likelihood may be hereafter, till 

 then, supposing the world should last 10,000 years ! 



3. Of optics, 3 books. — In the first he handles the simple and direct appear- 

 ances of objects, meaning such appearances as are not liable to reflection or re- 

 fraction. In the second, he handles the theory and practice of the perspective 

 or scenographic projection, or transcription of a given magnitude into a plain, 

 which cuts the optic pyramid ; wherein he explains the direct appearance, and 

 the monstrous deformation of an object, which at a certain place shall appear 

 beautiful. In the third, he treats of the astronomic projections of the sphere, 

 and thence derives the triple astrolabe, and shows their uses with the conveni- 

 ences or inconveniences of each projection. It is observed that the horizontal 

 projection is as ancient as Ptolemy, and all the four quadrants of several contri- 

 vances, published by Mr. John Collins, are derived from the western side, or 

 the continuance thereof, admitting but a mere mutation of the names of circles, 

 and a projecting of more parallels. 



4. Of catoptrics, 3 books — In the first of which the author treats of catoptrics 

 or reflection. In the second, of the affections of plain glasses simply, or of 

 many such placed either in a parallel or inclined position to each other. In the 

 third, of curved glasses ; and therein first the chief affections of convex spheric 

 glasses ; afterwards of concave spheric glasses ; lastly, of burning glasses of 

 several kinds. The death of the author prevented him from writing of the 

 dioptrics, which was very far advanced by Des Chartes, and has been since 

 further promoted by De Beaune, Honorato Fabri, Manzini, and in the cen- 

 tury of optic problems of Eschinard ; and we may hope that ere long the 

 learned Mr. Barrow will enrich the world with his labours of this and other 

 kinds ; also Mr. James Gregory, the author of Optica Promota, has a treatise 

 of this subject in good forwardness for the press. 



5. Follows the author's treatise of Military Architecture or Fortification. 



6. Follow his Annularia et Cylindrica; the first four books whereof were first 

 published in l651. 



Angeli not only answers what is objected by Tacquet against Cavaliri's Indi- 

 visibles, but shows what famous authors he has on his side, who have derived 

 many excellent inventions from this method of indivisibles, viz. Bcaugrand, 

 Rocca, Magiotti, Van Schooten, Rich. White, Bulliald, Torricelli, who calls 

 Cavaliri's first book the Ocean of Indivisibles, and the Fountain of Inventions. 

 Of which doctrine he renders many excellent examples. After many other ob- 

 jections and observations, the relator adds: All which is not recited here to dis- 



