(870 
% tfnefe being two ximita.hU Univerfal Rules in Geometry , tht fodder will fir.d the [ant 
(with many others) demonflrated by Dr. VVallis -in ku trea'ije De C a.'culc Cemr 
Gravitatis, which together withhis other Tracts , D« Mo:u, Statica } Mechanica 5 art 
now at the Prefs in London, the fame Kules are lificwije demonftrated in Geometric 
•parte Univerjali Jacobi Gregorii Scoti , Patavii 1660. Of which a competent number if 
£opiesis cxpeSed 'here. 
The Methods of thefe Learned Men are different , and good Arguments might begi- 
that they have not communicated nor feen the H'or\s of each other. 
., Guldinus , 1. 1. c. 1 2. JIhws a Mechanic^ way to find the Center of Gravity of a Sur- 
face or Curv'd Line, by 2 free fufpenfims , from the points of which , perpendiculars be- 
ing drawn , do crofs each other rtihe Center of Gravity, ihis we mention , to \eep the 
..Reader from tafangthe Center of Gravity of aCurv'dLine asfuch {which is intended 
. in this id Rule) to be the fame with the Center of Gravity of the Figure thereby termi- 
nated in the fir ft Rule. 
3. Confiders the ArTe&ions of Round Solids , begot from a Parabola > in 10 Propo- 
rtions from Numb. 20. to 29. both inclufive > whereof the 21 and 25 gives the Hoof 
required by Angelt, which was formerly cubed by Greg, de S. Vincxntio. In the 17th 
Prop, he gives the Proportion of the Parabolical Conoid to the SpUftdle made of the fame 
Parabola by rotation about itsBafe , tobe> AstheBffe of the Parabola is to of the 
*4xk 3 fhewing, that Guldinus err'd through forgetfulnefs. In Prop. 29. he delivers, that 
the Parabola bears fuch a proportion to a Circle defcrib'd abouttne B*/e thereof as a Diamg- 
Kr , As the Axis of the Parabola doth to that Circumference of a Circle, whofeR*- 
,Mus is equal to the diltence of the Center of Gravity of the Semi- Parabola from the 
-Axis. 
4. Contains divers endeavors and manifold new ways towards the obtaining the^*: 
Jyaturc of the Circle in 1 2 Proportions. 
5. Contains io PropofitionSj itom 41 to $1 ; in the.4ith whereof he find* a Spher t e- 
&<u&[to an Hyperbolical Ring-Solid > whence divers ways areopen'd towards the attaining 
the Quadrature of the Hyperbola : And he finds a Sphere equal to a Ring made by the 
, Rotation of a Segment of an Hyperbola 5 and of the Segment of a Circle thereto annexed, 
^efcribed about the Bafe of the. Hyperbola as a Chord Line : Then he abfolutely cubes cer- 
tain Hoofs cut out ©f an Hyperbolical Cylinder , and thenee derives other ways towards the" 
.obtaining the Quadrature of the Hyperbola. 
6. Delivers $ Theorems , ihewing the proportion between an Hyperbola and a Circle : 
* which are conceived to be wholly new. 
But thefe Hieorems fuppofethe Quadrature of both Figures known ,^ vi\. That of a 
* Circle 5 in requiring the length of the Circumference of ^Circle, delcribed bytheCmcr 
-of Gravity of anHyperbola; which Center cannot be found , without giving the Qua- 
■.draturem Areaoi the Hyperbola : which hath been mod happily perform'd by M. Mer~ 
cator in'his Logarithmo-Technia and further advanVd by Dr. WaHU in N. *8. of thefe 
-Tranftftions 3 and by M Gregorii alfo further promoted and otherwife perform'd in his 
lExcrcitationcs Geometric*, where he ihews 5 the fane Methods and Approaches to » be 
likewife applicable to the Circle. 
What we havefaid , being an Account of one of the moft confiderable Volumes of Ma- 
thematicks extant , we hope we may be the better excufed for prolixity. This Author for- 
* rncrly publiflVd the Elements of Plain and Solid Geometry in S 9 , and an Arithmetic^ 
in €• ., wherein he promifed a Treatife of Algebra. 
Errat. P. 865- 1. 24. r. m P C 3 p. 866. 1 3. del.finiflrorfum $ ibid. 1. 18. r. Gravi- 
tationem j ib. t. 24 -r> prsirejjivo j ib. L z).r. fit j p. 867. 1. 23. r.improprie. 
&j* P. 86$. Infert i&mediately before thefe words £ Lege fyllabAs^ Re- 
gala. Re, Se y fac'unt 0R-0S : Rofio faciunc <?5, eR. 
la the S A V o r, 
.printed by T. N. iotjohn Marty n , Printer to the Royal Society , and are 
to he fold mhe Befi a little without Temple-Bar , 1668. 
