Page:Philosophical Transactions - Volume 003.djvu/266

 eodem minorem. Sic $$ A:B::B= \frac{12C + 4B - D}{15}$$ minor erit quam arcus ABC; differentia autem in semi-circumferentia minor erit quam ipsius $1⁄1000$, & in quadrante minor quàm ipsius $1⁄60000$. Inter has approximationes sit maxima, penultima sex continue Arithmetice proportionalium, quæ minor erit quàm arcus, differentia autem, in semi-circumferentia minor erit quàm ejusdem $1⁄13000$, et in quadrante minor quàm ejusdem $1⁄3000000$. Sed hæc levia mihi videntur, cum possim Approximationes exhibere, quæ ab ipsa semi-circumferentia differant minori intervallo, quàm quælibet ejus pars assignata, neque nobis amplius apparent hæc mirabilia, cum demonstratio solida innotescat. Ad reliqua ab Hugenio publicata, cum à meo instituto sint aliena, nihil dico, nisi quod ipsa Hugenii dicta (non obstante exactissima sua, ut ait, materiæ hujus examinatione) à meæ Appendiculæ factis, ni fallor, longe superentur. Vale. Decemb. 15. 1668.

Figura Hugenii hæc est, quam ipse hoc sensu, licet Gal ice, sic explicat. Sit Arcus Circuli, qui non excedat semi-circumferentiam, ABC, cujus subtensa sit AC; & dividantur ambo in partes æquales per lineam BD. Ducta subtensa AB, capias inde, easque jungas inde ab A ad E in linea CA protracta. Dein, refecta lineæ DE parte decima EF, ducas FB, & tandem BG, ipsi perpendicularem: & habebis lineam AG æqualem Arcui ABC, cujus excessus tantillus erit, ut etiam tunc, quando hic arcus æqualis erit semi-circumferentiæ Circuli, futura non sit differentia $2⁄3$ suæ longitudinis; at quando non est nisi tertiæ partis circumferentiæ, differentia non erit $1⁄1400$; et si non sit nisi quartæ partis, non differet nisi $1⁄13000$ suæ longitudinis.

His Account is annexed to a Book, lately publisht in Latin by Dr. John Betts M. D. one of his Majesties Physitians in Ordinary, and Fellow of the London-Colledge of those of that Profession: In which Treatise (to touch that briefly) the Author endeavors to shew, that Milk, or something Analogous to Rh