In the latter part of his first Paper,
HE gives us (out of his Roset. Prop. 5.) this Attempt of Squaring the Circle. Suppose DT be• DC, and DR a mean proportional between DC and DT: the Semidiameter DC will be equal to the Quadrantal Arc RS, and DR to TV.
That the thing is false, is already shewed in the Latin Con∣futation of his Rosetum, published in the Philosophical Trans∣actions for July last past.
As it is now in the English; his Demonstration is pec∣cant in these words, (Col. 2. lin. 31, 32, 33.) Therefore - the Arc on TV, the Arc on RS, the Arc on CA, cannot be in conti∣nual proportion; (with all that follows:) There being no ground for such Consequence.
[And the thing is manifest; for since that, by his construction,
- DC.CA. Arc on CA extended ∷ are in the same continual proportion, of the Semidia∣meter to the Quadrantal Arc;
- DR.RS. Arc on RS extended ∷ are in the same continual proportion, of the Semidia∣meter to the Quadrantal Arc;
- DT.TV. Arc on TV extended ∷ are in the same continual proportion, of the Semidia∣meter to the Quadrantal Arc;
But (which is the common fault of Mr. Hobs's Demonstrati∣on) if this Demonstration were •ood, it would serve as well for any proportion as that for which he brings it. For if, instead of •, he had said, 〈…〉, or what else he pleased; the De∣monstration had been just as good as now it is, without chan∣•ing one syllable: That is, it will equally prove the propor∣t•on of the Semidiameter to the Quadrantal Arc, to be, what yu please.