404 PHILOSOPHICAL TRANSACTIONS. [aNNO I7OO. 



= AE, and join la : so is oc an indefinilely little particle of the arc coinci- 

 dent with its tangent. 



g. Because of the like segments ahIia, amoa, AmcA, as chord ac : to 

 chord lo :: so is arc Axnc = amc : to arc amo. Or ac : ao :: xmc = amc 

 : AMO. And dividing ac — ao (= co) : ao :: Amc — amo (= co, : amo. 

 That is, CO : ao :: CO : : amo, and alternately, co : co : : ao : amo. Put ac for 

 AO, and AMC for amo (as differing infinitely little) and then it is co : co : : ae : 

 AMC But by construction cl = ae = amc ; whence co : co :: ac : cl, and 

 the angle lca = coc, (oc being infinitely near to ac, is therefore parallel to 

 it,) and therefore coc, acl are similar triangles. 



10. Because of cl =: ae, ang. eac =: lca, (cl and ea being tangents to 

 the two ends of the same circular arch amc, make equal angles widi its chord 

 AC,) and AC common to both, the triangles eac, acl are like and equal : 

 therefore are all three coc, acl, eac, like triangles. Whence it follows, that 

 the angle ace, in the triangle eac, is equal to the angle occ, in the triangle 

 coc. But occ = ACT, because oc and ac are parallel ; therefore ang. ace = 



ACT. Q.E.D. 



On the Circulation and Stagnation of the Blood in Tadpoles. By M. Lemvenhoeck. 



N° 260, p. 447. 



M. Leuwenhoeck procured tadpoles of several sizes, the largest were arrived 

 to such a magnitude, that their hinder legs stuck out from their bodies ; and 

 of the smallest 30 of them together made but the size of one great one : 

 hence we must conclude, tliat the frogs lay their eggs, but very slowly ; for 

 it was already about a month's time since he had made his observations, when 

 some amongst them appeared to be half grown. 



The first observation he made of the motion of the blood, was in a small 

 vessel, that was a little wider, than that a red globule of the blood could go 

 through it, as A and b, fig. 9, pi. 11. This vessel, which is an artery, through 

 which the blood coming from the heart from a to b, is impelled with great 

 swiftness, divides at b into two branches, bc and be. These two branches 

 united again at d, where they continued united but a little way, from d to f, 

 after which it divided again into two branches, fg and pi. These two branches 

 run crooked, and were united again at h, where they made again somewhat a 

 larger vessel, hk, and at k it united again into a larger vessel. Hence we must 

 call these blood vessels, abcdfg and abepi, arteries, because they carry the 

 blood from the heart first in g and i ; and the blood vessels ghk and ihk we 

 must call veins, because they convey the blood to the heart again. 



In another place Mr. L. saw the blood run in au artery that was so large. 



