■ (-■2055 ) 
5* Of Triangles and Right- lined Figures^ 
6.- Of Circles, where he delivers the Dodrineof the third 
hook oiE^iclzd*^ and, imitating Archimedes enlargeth this 
Chapter with other propertys, which he had firft fiiewo to be 
congruent to Right-lined Figures* 
7* He treats of Problemes, by which a Preparation is made 
to pafs from Speculation to Life and Pradice. 
The Author having thus altered Euclid's order ) giveth an 
Index^ to (hew where the Propofitions of the i,^, 33 5 and 6tK 
Book of Euclid are to be found in thefe Elements. 
He hath pafied over all the Propofitions of the 4^^. Book of 
Euclid, as fuperfluous in his method : In that Book, 'tis known, 
thdit-Euclid teacheth. How to Infcribe or Circumfcribe feme ^hut 
not ^/y Regular Figures about a Circle: Of this he treats at 
the end of the yth. Chapter. This Dodrine is either neceflary 
for Pradice^ as 10 Fortification ; or in order to the Conftruftion 
of the Canon of Sines^ He intends to treat of trigonometry and 
Fra&icalGeofnetry elfewhere, faying in his Dedication 5 
Euclidem ex novo adornare fludui^ brevi tamen fcripione eon^ 
cinnaium , ut ejfet cfportnnior. Ex quo tanquam exfundamento 
f^endet reliqua mearum doUrina tra&ationum , quas prMo paratas 
me habere probe nojii^ As to his method of Demonftratioo^ he 
faith, Demonjirationes vix alias pono^ quam afirmativas^ utdifi 
centibus confiet^ea qu£ proponuntur non tantum vera ejje^fedetiam 
cur vera fint : in Euclide non pauca per negativas dentonjiratto-' 
nesprobantur , velinhk probanda negative tantum probata af- 
fumuntur , C^^ An recfe omnia ^ nonnulli controvertunt , 
III SYNOPSIS G EO METRIC A'y cum Tr^bus Opufculk ^ 
De LINE A SiNVVMd' CTCLOIDE ^ De MAXIMIS & Aih 
. NIMIS^ Centuriay Et STNOPSIS GEOMETRIJS PLANjE ^ 
Honor* Pabr^ S^JeJk, Lugduni Gailiarum 1669. in 12" ^ 
'^'~|^His Author in this Geometrical Sjnopjis hath endeavoured, 
as M, Gottigniesj ( jufi: now taken notice of^ ) c v .mifeth 
to do in his New Euclid^ to render Geometry dearer it d eaher 
by delivering fuch Demonftrations, as prove the thing in hand 
by JireS znd intrinficli Principles, not fuch as are indirefl:, and 
leading adabjurdum impojfibile^v^h^vehy 'ds only eluded, 
that the thing cannot be falle^ but not fhewn, why it is and muft 
be true. la reference to which; he confidcrs^ that, whereas Gi^o- 
N a milr^ 
