W + i^' 4- t| + ,\l A' \ TTfl &c, 
aad the Natural Secant to xhQ faif^Arch 
I + T + 7?; + tiji ' $cc. 
and from the ArithmetiQk of Ififini^es, the Ntimber of thefe 
Secants being the Arch A, it follows, that the fum Tcx^l 
of all the Infinite Secants on that Arch is -li- 
>4 + 4 4- + &c. , 
the which, by what foregoes, is the Logarithm Tangent ^ of 
Napeirs form, for the Arch of 45''+ k A as before. 
And Colleding the Infinite Sum of all the Natural Tan- 
gents on the faid Arch Ay there will arifc 
twhich will be found to be the Logarithm of the Secant rf 
he fame Ardi 
Accounts of Booka. 
^ide Gregono^ D. M. Afironomt^ Frofejjhre 
Samiiano Oxmi^^ ^ Sif€. Keg. Socio^ S"". 
I "fhiAf^o Oxon. 5> 
tills ^eati^ the Leiarhecl Xitfibr ^ei^ the 
JH Pf iflcipal Laws of Refleftioa and ttefra<aion, with- 
out reftraining bimfetf to aay Sect of Pbilofcphears^; as 
a!fo the prof>erties of plain ^d fpherkai Surfaces in rc- 
ftedingand refrading of Rays, and by the way Ibews 
how it comes that Ipherical Surfeces produce the fame 
effed3 with thofe of certain Sphercrids^nd Conoids, viu 
becaufe they have the fime degree of Cumtin?e. la 
the Gatoptricks he determines the pbce of the Image, 
when the. Objeft an4 the Eye-ar^ not la the fime 
axis of the reflecting Sphere : an inconvenience that 
Dioptrical Machines are tipt fubjeft tc. . 
Then he proceeds to determine the fituation and big* | 
nefs of the Images of fenfibly big Objefts, with the j 
quan--! 
