Encyclopaedia Britannica, or, a Dictionary of arts, sciences, and miscellaneous literature : enlarged and improved. Illustrated with nearly six hundred engravings > Volume 19, Scripture-SUG

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iimlbn. portion tliat had ever been exhibited to the phyfico-ma-
—thematical philofopher and he ufed always to illu-
ftrate to his more advanced fcholars the fuperiority of
the geometrical over the algebraic analylis, by compar¬
ing the lolution given by Newton of the inverfe pro¬
blem of centripetal forces, in the 42d propofition of that
book, with the one given by John Bernoulli in the Me¬
moirs of the Academy of Sciences at Paris for 1713.
We have heard him fay, that to his own knowledge
Newton frequently inveftigated his propofitions in the
fymbolical way, and that it was owing ehielly to Dr
Halley that they did not finally appear in that drefs.
But if Dr Simfon was well informed, we think it a
great argument in favour of the fymbolic analyfis, when
this molt fuccefsful practical artijl (for fo we mult call
Newton when engaged in a talk of difeovery) found it
conducive either to difpatch or perhaps to his very pro-
grefs.
Returning to his academical chair, Dr Simfon difehar-
ged the duties of a profeffor for more than 50 years with
great honour to the univerlity and to himfelf.
It is almolt needlefs to fay, that in his prelections he
followed ItriCtly the Euclidian method in elementary
geometry. He made ufe of Theodofius as an introduc¬
tion to fpherical trigonometry. In the higher geome¬
try he preleCted from his own Conics ; and he gave a
fmall fpecimen of the linear problems of the ancients,
by explaining the properties, fometimes of the conchoid,
fometimes of the cifibid, with their application to the
folution of fuch problems. In the more advanced clafs
he was accultomed to give Napier’s mode of conceiving
logarithms, i. e. quantities as generated by motion; and
Mr Cotes’s view of them, as the fums of ratiunculae ;
and to demonftrate Newton’s lemmas concerning the li¬
mits of ratios; and then to give the elements of the
fluxionary calculus; and to finilh his courfe with a fe-
le£t fet of propofitions in optics, gnomonics, and central
forces. His method of teaching was Ample and perfpi-
cuous, his elocution clear, and his manner eafy and im-
preflive. He had the refpeCI, and Hill more the affec¬
tion, of his fcholars.
With refpeCt to his ftudies, we have already inform¬
ed the reader that they got an early bias to pure geo¬
metry, and to the elegant but fcrupulous methods of the
ancients.
We have heard Dr Simfon fay, that it was in a great
meafure owing to Dr Halley that he fo early direCted
his efforts to the reftoration of the ancient geometers.
He had recommended this to him, as the molt certain
way for him, then a very young man, both to acquire
reputation, and to improve his own knowledge and tafte,
and he prefented him with a copy of Pappus’s Mathe¬
matical Colle&ions, enriched with fome of his own notes.
The perfpicuity of the ancient geometrical analyfis, and
a certain elegance in the nature of the folutions which
it affords, efpecially by means of the local theorems,
loon took firm hold of his' fancy, and made him, with
the fanguine expe61ation of a young man, direft his very
firft efforts to the recovery of this in toto; and the refto-
, ration of Euclid’s Porifms was the firft tafk which he
let himfelf. The accomplifhed geometer knows what a
defperate tafk this was, from the fcanty and mutilated
account which we have of this work in a fingle paffage
of Pappus. It was an ambition which nothing but fuc-
cefs could juftify in fo young an adventurer. He fuc-
ceeded; and fo early as 1718 feemed to have been in
complete polfeflion of this method of inveftigation,
which was confidered by the eminent geometers of an¬
tiquity as their fureft guide through the labyrinths of
the higher geometry. Dr Simfon gave a fpecimen of
his dilcovery in 1723 in the Philofophical Tranfatf ions.
And after this time he ceafed not from his endeavours
to recover that choice collection of Porifms which Eu¬
clid had collected, as of the molt general ufe in the fo¬
lution of difficult queflions. Wnat fome of thefe muft
have been was pointed out to Dr Simfon by the very na¬
ture of the general propofition of Pappus, which he has
reftored. Others were pointed out by the lemmas
which Pappus has given as helps to the young mathe¬
matician towards their demonltration. And, being thus
in pofleflion of a confiderable number, their mutual re¬
lations pointed out a fort of fyitem, of which thefe made
a part, and of which the blanks now remained to be
filled up.
Dr Simfon, having thus gained his favourite point,
had leifure to turn his attention to the other works of
the ancient geometers; and the porifms of Euclid now
had only an occafional ffiare. The lociplani of Apol¬
lonius was another tafk which he very early engaged in,
and completed about the year 1738. But, after it was
printed, he imagined that he had not given the ipfijjimcz
propojitioncs of Apollonius, and in the precife fpirit and
order of that author. The impreflion lay by him for
fome years ; and it wras with great reluCtance that he
yielded to the intreaties of his mathematical friends, and
publifhed the work, in 1746, with fome emendations,
where he thought he had deviated fartheft from his au¬
thor. He quickly repented of this fcanty conceflion,
and recalled v;hat he could of the fmall number of co¬
pies which he had given to the bookfellers, and the im¬
preflion again lay by him for years. He afterwards re-
correCted the work, and ftill with fome reluCtance al¬
lowed it to come abroad as the Reftitution of Apollo¬
nius. The public, however, had not been fo faftidious
as Dr Simfon, and the work had acquired great cele¬
brity, and he was now confidered as one of the firft and
the molt elegant geometers of the age: for, in the mean
time, he had publifhed his Conic Sections', a work of
uncommon merit, whether we confider it as equivalent
to a complete reftitution of the celebrated work of A-
pollonius Pergaeus, or as an excellent fyftem of this im¬
portant part of mathematics. It is marked \vith the
fame features as the loci plani, the moft anxious folici-
tude to exhibit the very text of Apollonius, even in the
propofitions belonging to the books which had been
completely loft. Thefe could be recovered in no other
way but by a thorough knowledge of the precife plan
propofed by the author, and by taking it for granted
that the author had accurately accomplifhed this plan.
In this manner did Viviani proceed in the firft attempt
which was made to reftore the conics of Apollonius ;
and he has given us a detail of the procefs of his conjec¬
tures, by which we may form an opinion of its juftnefs,
and of the probability how far he has attained the de-
fired objeCt. Dr Simfon’s view in his performance was
fomething different, deviating a little in this one cafe
from his general track. He was not altogether pleafed
with the work of Viviani, even as augmented by the
eighth book added by Halley, and his with was to re¬
ftore the ancient original. But, in the mean time, an
3 A 2 academical