306 PHILOSOPHICAL TBANSACTIONS. [aNNO I706. 



V rise the perpendicular vw ; from a draw aw perpendicular to the tangent ad, 

 till it meet vw in w. So is aw the radius of the curvature at a. 



VIII. This curve may be continued on infinitely above the point p, but by a 

 different and more operose way of construction ; the properties of which will 

 be these. 1 . The difference of its tangent and subtangent (taking the subtan- 

 gent in the line hs) will be always equal to the same given line fh or a. That 

 is, as i -|- ^ := «, below p, so / — s •=. a above f. 2. A^ below p the curve line 

 is equal to the sum of its ordinate and subtangent, so above, it is equal to their 

 difference, or s — • ^. 3. As below p, 'lay = ilm, so above, lay = \x^. All 

 which, and its other properties, may be demonstrated as the preceding, mutatis 

 mutandis. 



IX. With a little variation in the foregoing construction, may the logarithmic 

 curve be constructed, which is also a quadratrix to the hyperbola. In fig. 8, 

 omitting the string mrp, let the distance mr be equal to the subtangent of the 

 intended logarithmic curve, which is invariable ; stick a pin at r in the ruler 

 CD, to which apply the ruler ep, so that the ^A^(^ of the little quadrant hi rest- 

 ing on the ruler ab, the distance ri may be equal to mr. Then keeping the 

 ruler ep tight to the pin r and ruler ab, slide the ruler cd along in a straight 

 line by the ruler or line so; so will the wheel ^h describe a part of the loga- 

 rithmic curve TV, whose subtangent is every where mr. 



X. In fig. 9> let PAE represent the logarithmic curve, whose subtangent is 

 equal to ph. lix is an equilateral hyberbola, &c. as before in ^ Jii. Let pg 

 = ar, GA = yt ph = bd = a, gh (= ls) = a — ar, ac = x, ca = y. Then 



AC : ca :: ab : bd, that is, i* : ^f :: a — x : a :: a : ; therefore ay = x. 



The flowing quantity of a^r is ay; and the flowing quantity of — — - .r is the hy- 

 perbolic area pilg, for by the nature of the hyperbola gl = ; therefore is 



the hyperbolic area filg, equal to ay, a rectangle whose sides are the sub- 

 tangent bd = ph, and ordinate ga (as here accounted) of the logarithmic curve. 



y^ Account of a Booh, viz.-^Samuelis Dale, Pharmacologii;e seu Manuduclionis 

 ad Maieriam Medicam Supplementum : Medicamenta Officinalia simplicia, 

 priore Lihro omissa, complectens : ut et Notas Generum Characteristicas, Spe- 

 cierum Synonima, Differentias, et Fires. Cum duplici Indice, generali altera 

 Nominum et Synonymorum prcecipuorum, altero Anglico- Latino, in gratiam 

 Tyronum. N° 306, p. 2263. 



In the year 1693 our author published his Pharmacologia seu Manuductio ad 



