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iind though ardently Jefirous to elevate hhnWr to the catiTc 

 of tht pheiiomeiin, is equally apprehenfive that he may be 

 miilaiitn in tliat which lie alligns to them. Kepler owed to 

 nature the liril of thcfe advantages, and the fecond to Tycho 

 Brahe, who perceived his genius, and adviUd him to abandon 

 his attachment to the niyllerious analcjnes of fig\ire3 and 

 numbers to wliich he was then addifted, and to attend more 

 clofelv to fatts and their confequences. This appears to 

 have had its proper cfFeft, and Tycho dying a fcv- years af- 

 terwaras, Kepler was put in poffeirion of his collection of 

 obfervations, which he employed to the moft ufcful purpofes, 

 havinir founded upon them three of the moll important dit- 

 coveries that have ever been made in natural philofophy. 



It was an oppofition of Tvlars, which determined him to 

 occupy himfelf, in preference, upon the motion ot this pla- 

 net ; and being then llrongly attached to the Ptolemaic fyf- 

 tem as modified by Tvcho llrahc, as well as to the opinion 

 which had hitherto been generally received, that all the ce- 

 Icftial motions mud be pcrfettly circidar and uniform, he 

 endeavoured, for a long time, to rcprefent thofe of Mars 

 according to this hypothefis. At kngth, however, after 

 many trials of this kmd which he has given in detail, in his 

 treatife called "Stella Martis," he difcovered that the orbit 

 of Mars is an elliplis of which the fun is placed in one of the 

 foci, and that the planet moves in it in fuch a manner, that 

 the radius veftor, or a line drawn from the centre of the fun 

 to that of the planet, defcribes areas proportional to the 

 times. This law he alfo foon afterwards extended to all 

 the planets; and in 1(126, he publiflied, according to this 

 theory, his Rudolphine tables, wdiich will be for ever memo- 

 rable in aftrononiy, as being the firll that were founded on 

 the true laws of the planetary motions. 



It is here worthy of remark, that without the fpecnlations 

 of the Greek mathematicians, upon the curves formed by the 

 feftions of a cone, it is highly propablc that we Ihould yet 

 have remained ignorant of iome of the moll curious and im- 

 portant laws of nature The ellipfe being one of theie 

 curves, its lengthened figure fuggelled to the mind of Kep- 

 ler the idea that the planet Mars, whofe orbit he had found 

 to be more oval than circular, might poffibly move in it ; 

 and foon after, by means of the numerous properties which 

 the ancient geometers had dilcovered of the conic ftftions, 

 he affnred himfelf of the truth of this hypothefis. The 

 hiftory of the fciences affords many examples of this kind 

 of application of pure geometry, and of the advantages 

 attending it ; for every thing, in the immenfe chain of 

 truths, is connefted ; and frequently a fingle obfervation of 

 apparently trifling confequence, has led to a more intimate 

 knowledge of nature, of which the pha;noinena are the 

 mathematical refults of a fmall number of invariable laws. 



The perception of this truth was probably what fiift 

 gave rife to the myilerious analogies of the Pythagoreans ; 

 and Kepler, who had indulged himiclf in refearches of this 

 kind, was indebted to it for one of his moll brilliant difco- 

 veries. Being perluadcd that the mean diftances of the 

 planets from the fun ouglit to be conformable to thefe ana- 

 logies, he compared them, for a long time, both with the 

 properties of the five regular bodies, and with the notes of 

 mufic. At length, alter feventecn years of meditation and 

 calculation, having had the idea of comparing them with 

 the j)owers of the numbers by which they are expreffed, he 

 found that the fquares ot the times of the revolutions of the 

 planets are to each other as the cubes of their mean dillances 

 from the fun; and that the fame law applies equally to their 

 fatellitcs. 



Aftronomy is Ilkewilc indebted to Kepler for fevcral other 

 difcoveriesj which, though not equal to the former, Me 



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dill of confiderable importance. He believed that it was 

 the attraction of the moon which caufed the flnx and reflux 

 of the ocean ; and he had fo far an inlight into the general law 

 of gravitation, as to fnlpedl, that the irregularities of the 

 lunar motions were occaiioned by the combined actions of 

 the earth and the fnn. In his work on Optics, he has alfo ex- 

 plained the mechanifm of vltion, which was before unknown ; 

 and in another performance, called "Stereometiia Doliorum," 

 he has preiented feveral views on the nature of infinites, which 

 had confiderable influence on the revolution that geometry 

 underwent about the end of the lall century. 



It is afflicting to relate, that this great man, who may be 

 confidercd as the founder of modern ailronomy, had his lall 

 days embittered by the horrors of poverty and dillrefs. A 

 fmall penfion, which was fcaicely fufiicicnt for his lubfitlence, 

 vvai frequently withheld or unpaid ; and the trouble and 

 vexation which this occafioned him, obfcured his genius, 

 and fliortenedhis exiftence. He died on thel5tli of Novem- 

 ber 16^1, m the fifty-ninth year of his age, leaving nothing 

 for his wife and family, but the glorv' ot his name, and the 

 fame he had fo jullly acquired; but as thefe were infufficicnt 

 to relieve his own wants, they could afford but little com- 

 fort to a helplcls wife, and her wretched off^spnng, whofe 

 indigence is faid to have been fuch that they had not even 

 the common ncceiraries of life. 



In the time of Kepler, there were not wanting feveral 

 other confiderable proficients in ailronomy. Edward 

 Wright, an Englifliman, made feveral good meridian obfer- 

 vations of the fun, with a quadrant of fix feet radius, in 

 the years 1594, 1595, and 1596, from which he improved 

 the theory of the fun's motion, and computed his declina- 

 tion more accurately than had been done before. He alfo 

 pnblidied, in 1599, an excellent work, entitled, "Certain 

 Errors in Navigation difcovered and detefted ;" containing 

 a new method of projettlng maps and charts, which liaa 

 commonly, though crroneouily, been afcribed to Mercator. 

 The fcience is alfo greatly indebted to baron Napier of 

 Scotland, not only for his ever memorable invention of loga- 

 rithms, which has fo wonderfully facilitated the bufinefs of 

 calculation, but for fome excellent theorems and improve- 

 ments in fphcrics. About this time, likewife, Bayer, a 

 German, publiflied his "Uranometria," orcom])lete Celeftial 

 Atlas, containing the figures of all the conilellatious \ifible 

 in Europe; into which he introduced the highly ufeful in- 

 vention of marking the ftars by their names, or the letters 

 of the Greek alphabet, which renders them fo eafy to be 

 referred to with dillinctncfs and precifion. 



At the fame time alio, that Kepler, in Germany, was 

 tracing the orbits of the planets, and fettling the laws of 

 their motions, Gahleo (who was born at Pifa, in Italy, in 

 1564) was meditating upon the doftrine of motion in ge- 

 neral, and invelligating its principles ; and from the admir- 

 able difcoveries which he made in this branch of the phyfico- 

 mechanical fciences, Newton and Huygens were afterwards 

 enabled to derive the moll brilliant and complete theories of 

 all the planetary motions. About this period alfo, a fortu- 

 nate accident produced the moll marvellous inflrumeiit that 

 human induftry and fagacity could have ever hoped to dif- 

 covcr ; and which, by giving a far greater exteiiilon and 

 precifion to allronomical obiervations, ftiewcd many irregu- 

 larities and new phaenomena, which had hitherto remained 

 uidcnown. 



This invention was that of the telefcope, wh'ch was no 

 fooner known to Galileo, than he fet himfelf about to im- 

 prove it ; and the dilcoveries he was by this means enabled 

 t(J make, were as new as they were furpriiiiig. The face of 

 the moon appeared full of cavities and afperities, refeinbi'ing 



vallieG 



