38 PHILOSOPHICAL TRANSACTIONS. [aNN0 1672. 



As soon as these frosts were over, we had glowing heats, which caused a 

 general complaint amongst us of excessive sweating, by night and day. The 

 bushes and many flowers in the garden appeared in such forwardness, as if it 

 were in April or May. I saw young coleworts growing; roots and leaves; on 

 the top leaves of an older colevvort. Not far from my abode, an apple-tree 

 blossomed before Christmas. 



In old histories I find, that earthquakes, inundations, droughts, famine, 

 pestilences, were each of them, in their several seasons, and sometimes one 

 close on the heels of the other, almost universal over the known world; some- 

 times raging from place to place several years together. As the learned Meade 

 relates of a pestilence, which, in the days of Gallus and Volusianus, began in 

 Ethiopia, and for 15 years wasted all the Roman provinces. 



A Method of Draiuing Tangents to all Geometrical Curves , hy M. Ren. Fr. Sluse, 

 Canon of Liege, in a Letter to the Editor, N° QO, p. 5143. Translated from 

 the Latin. 



I send you. Sir, my method of drawing Tangents to any Geometrical Curve 

 whatever, and submit it to the censure of the learned men of the Royal Society. 

 It appears to me so short and easy, that it may be learned by a novice, and with- 

 out the labour of any further calculation extended to all kinds of lines: but I 

 wish rather to have the approbation of others, since we are commonly too partial 

 to our own inventions. 



Let any curve DO (Fig. 1, PI. 1,) be given, all the points of which are re- 

 ferred to any given right line E AB, by the right line A D ; it matters not, whe- 

 ther E AB be a diameter or any other line, or whether there be also given other 

 lines, which, or their powers, may enter the equation. 



In an analytical equation, for greater plainness, let DA be always designed by 

 i;, BA by 7/, and let EB and other known quantities be expressed by consonants; 

 then let DC be supposed drawn, touching the curve in D, and meeting EB pro- 

 duced, if needful, in the point C; and let C A be always called a ; then this will 

 be the general rule for finding C A or «. 1. Reject out of the equation all those 

 members, in which neither y nor v is found ; then put all those terms that have 

 y, on one side ; and all those which have v, on the other, with their signs + or 

 — ; and let the latter for distinction and ease sake be called the right, the for- 

 mer, the left side. 2. On the right side let there be prefixed to each member 

 the exponent of the power which v has there ; or, which is the same, multiply 

 all the members into that exponent. 3. Let the same be done also on the left 

 side, multiplying each member there by the exponent of the power of ?/ therein; 

 and besides, let one y in each member be always changed into a. — The equation 

 thus transformed shows the method of drawing a tangent to the given point D. 



