(88a) 
An ExtraSl 
* fouma dss <of ALtttertif Mr . James Gregory to the P»Mi(her] containing (*me 
Noven.i2f Conftderations of his y upon M. Hugens his letter, printed* in 
i*68. Vindication of his ExamenoftheBook, entitled Vera Circu'i & 
Hyperbola Qiiadratura. 
^T^He firft occafton of the exchange of Letters on this Subjesl was given in 
JL the Journal des Sea vans of July 2. 1668. to which a civil return duos 
made in Numb. 37. of thefe Trails : which having be^n jtdicioufly animad- 
verted upon in another Journal des Scavans, viz. of No \ 12. 1668. 'it was 
thought equitable here to make publicly what M. Gregory hath fince impart- 
ed thereupon, out of a de fire exprejfedby him, further to elucidate that con* 
trover fie. which how fatisfatlory it is, we leave to the intelligent to judge 
prof e fling, that we are no further concerned in this contefl, than to let the Sa- 
gacious Reader know the proceedings thereof, by referring him to the French 
Journals about Vehat is fold thereof on the one hand, and by delivering in thefe 
Papers, what comes from the other : which as *tis intended to be done without 
any ammo fity or offence, fo we defire the Candid Reader Will pardon us for di- 
verting him thus much by this dtfpute from what elfe he might jufily expetl in 
thefe Philofophical Occurrences. The Anfwer it J elf of _M. Gregory,' fol- 
lows in the fame language, therein he thought fit to communicate it, viz. 
Exduobus Argumentis, quibus conatur Nob. D. Hugenius ido&rinam' 
meam evertere , prirno quidem , refponfionis fundaxnentum dedi in Pro- 
«e*». ad Geom. partem univerfalem : alteram autem provenit folummodo a 
Prop. 11. non rede, opinor^ &bHugenio intelle&a. quam tandem admittic 
poft Corrediones (ut intuit ) a me fa etas. Ut autem , (imal cum refoluti- 
one Obje<ftionum , omnem evertam dubitandi rationem , ex admiffa 
Prop. 1 i ma . in forma conabor probare fyllogiftica , Nullam effe rationem 
Analyticam inter Circuiumet diametri Quadratum : praeter Modum quip- 
pe et Figur&m nil deeft in haftenus a me pubiicatis , quin id integre 
demonftrciur ; quae interim forma raro a Geometris exigitur. Dico 
itaque-, 
Si darettir ratio Analytica ( feu ratio notis Analyticis exprimendaj 
inter G'rcuium et Diametri quadratum , tunc Circulus analytice compo- 
neretur ex Quadratis, inferipto & circumfcripto. Sed pofterius eft abfur- 
*lum. E. Sequela Major is fie probatur ; 
Quantitas quaefita & determinata invenitur ex quantitatibus quibufcun- 
queram determinantibus 5 in ea ratione, feu relatione quam habet quantity 
determinata ad di&as quanricates determinantes. Sed Quadratum inferip- 
tum & circumfcriptumCirculum determinant, ideoqucex illis Circulus da- 
recur in ea relatione , quam babet ad diametri Quadratum vel ejus fe 
mifTem 
