Page:Philosophical Transactions - Volume 003.djvu/262



He first occasion of the exchange of Letters on this Subject was given in the Journal des Scavans of July 2. 1668. to which a civil return was made in Numb. 37. of these Tracts: which having been judiciously animadverted upon in another Journal des Scavans, ''viz. of'' Nov. 12. l668. it was thought equitable here to make publick, what M. Gregory ''hath since imparted thereupon, out of a desire expressed by him, further to elucidate that controversie. Which how satisfactory it is, we leave to the intelligent to judge; professing, that we are no further concern'd in this contest, than to let the Sagacious Reader know the proceedings thereof, by referring him to the French Journals about what is said thereof on the one hand, and by delivering in these Papers, what comes from the other: which as 'tis intended to be done without any animosity or offence, so we desire the Candid Reader will pardon us for diverting him thus much by this dispute from what else he might justly expect in these Philosophical Occurrences. The Answer it self of M. Gregory, follows in the same language, wherein he thought fit to communicate it,'' viz.

Ex duobus Argumentis, quibus conatur Nob. D. Hugenius doctrinam meam evertere, primo quidem, responsionis fundamentum dedi in Proem. ad Geom. partem universalem: alterum autem provenit solummodo à Prop. II. non recte, opinor, ab Hugenio intellecta, quam tandem admitti: post Correctiones (ut inquit) a me factas. Ut autem, simul cum resolutione Objectionum, omnem evertam dubitandi rationem, ex admissa Prop. IIma. in forma conabor probare syllogistica, Nullam esse ratíonem Analyticam inter Circulum et diametri Quadratum: Præter Modum quippe et Figuram nil deest in hactenus à me publicatis, quin id integre demonstretur; quæ interim forma raro à Geometris exigitur. Dico itaque.

Si daretur ratio Analytica (seu ratio notis Analyticis exprimenda) inter Circulum et Diametri quadratum, tunc Circulus analytice componeretur ex Quadratis, inscripto & circumscripto. Sed posterius est absurdum. F. Sequela Majoris sic probatur;

Quantitas quæsita & determinata invenitur ex quantitatibus quibuscunque eam determinantibus, in ea ratione, seu relatione quam habet quantitas determinata ad dictas quantitates determinantes. Sed Quadratum inscriptum & circumscriptum Circulum determinant ideoque ex illis Circulus daretur in ea relatione, quam habet ad diametri Quadratum vel ejus