For the North Carelna Standard


The Origin and ProgreSsaDf Mathematics
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For the Nertl1 Carolina Standard ,
The Origin and Progrsss.nf Mathematics.


fs sNos. - a8ttss


Hippocraies'of Ghios who Iixed b. &C. 45o, wfote
an elementary treatise on geometry, which is lcsi


he was one ot the geosnetEciaas csxh9 attempted
TO solve the Probfemlof toe duplication offhe cube.
Che object OF this ProbleE was to consruct cube
which should be doubieahe weight sf a viFen cube


that Is when both were composed Of like :subseaa-
ces. This problem. was 10 be solved without GIN


ploying any instEuments other than The square and
compasses, as no: operations were considered ge-
t9etEieal except Shase peEforIned by the use of
these instruments alone; all eihets being considers
ed mechanical 1t Is said that Apollo; in ofdeE TO
revenge insult, afflicted the -Athepians wish n
direfnt pestteBee, andthe Oracle Of Deiphos being
Ecopsulted concerning. The means of alDeasins


him answered. double she aliaIs,.s Now the altar
Of Apollo at Athens, which was alluded 10, -xas-a
cube. The priests of polio not entfreI1 fprseltiht
ttFir oEa intetesi,-reqlired the new altar togbe
composed Of gold, but this did not increase the diff
ieultY of the probleIn Ptaio B. c. 800 ffnitIess-
lY endeavoEed to solve It by means of tie square
fAnd co1ipasses, though he sureeeded in discover
ting solution Of the mechahieal kind. He was,
BESIDES being philosopher, q greargeometTicfan !;
indeed so fully was he impressed with the7fnpoF-
ttahce OF this science1ha he wrote over his door


" let % one enter here who is igDorant-of Seome-
iry: Before the time of Pia1o the only curve


made use of in geometry was the ciIcie, he in1ro-


duced the theory of comic spelons these are coges
found BY cutting cone by aplanel lh aifftrp nj


directions. He discovered a great many -pEoper-


t,es belonging TO these curves, and bis scholars,


Aristeus, Menechmus, DinestEatus and others PEN


etrated deeply into this brancof science Arisians
composed five books on COMIC sections svhich.Un.
fortunately are Lost, [Menechmps made two appf-


cations of them TO rhe duplication of the eabe, bat


though they were perfectin theory, there then ex-


listed no instruments by which such sections could


be made The problem offhe tri-secton OF al angle


was also discussed in the school Of Pato Diaos-
ttratus discovered acurve which WORLD have solved


both the problems and answered .4he conditions, If


It coutd have been. described by one continued
motion OF Ihe square and camPasses. The ancient
geometraflans-we possessed with the idea that


these problems could be determined by The use of


the Square and cotnpasses alone, bat the experience
| OF many centuries and7of many great Faatheniati-


clans who have spent nearly i6sir whole hives in


endeaVorlng to solve them, has shown TO the con-


trary, and they have at, last beeu- reIinquished


The dscusslo1 of ihesel points has however been
OF grea: use to geometEy, since ia attempting TO
sotye tRem, sgeometrcians have discovered truths


OF farmore value TO Ihemattes than the solution
Fof either would have been had il beeRfound.-'


Thales, PyIhagoIos and others Of his predecessors


had discovered manvtf the funddm email p-inc cples


OF geometry, but to Euclid is due the credit of first
reducing 10 a science. His .eleinPnIs of geome-


try so completely answered. the purpose for which


they were written thai they used for upwards
OF Two thousand years, exclusively in all mathe-


NAUTICAL schools, by all nations, and translated nto
all 1angaages-a greater comp Uncut than can be
paid to any other work on any subject Euclid in


demonstrating confined himself 10 the strict method


OF the ancents, which often his demon stra-


tions long Indirect and tedious. On this aceount
LeSendre's geometry in which more simple and
easy demonstrations are used IS now preferred TO


Euclid's. Euclid was tutor in mathematics to


Ptolemy Lagos. king of Egypt. man of sense and
learning, who,obserVing 1he difficulty above men


toned, and tired of immense labor in p9Tsuing The


subject asked Euclid if he could not render theay
for Aa
IL No, Sire, there is no-tovaf road 10 geometry" /"
Euclid lived Be-. $50. He was the founder of
the school at Alexandra, Of which city re was


native. History is silent TO the time Of Enclid's


death. He is represented "a man of courteous
and agreeable behaviour, and in great esteem with
King Ptole1nY. - ~' =


tArchimedes, the greatest mathematician or an
iquity, who Aourished B. C. 250 was the frs. p4Io
discovered the approximate ratio, which the cir,
conference OF circle bears 10 its diameter. He
also determined the ratio which The sphere and
cylinder bear 10 each other. He made great
many important discoveries IN comic seeIions and
extended and demonstrated the use of geomeiTicaI
analysis. the principles of which had before cen
given by the school Of Plato. Indeed volume
might be written concerning the works Of this 1ru


" great man. We are told that Archimedes at
first made record Of his discoveries but delight
ed in keeping the whele chain of problems in his
mind and pursuing his researches without the aid
of notes. He afterwards committed them to writ
ing for the use Of mankiHdf 70 show King Hiecro
the wonderful effects Of mechanical power he is
said TO have, by the aid Of ropes aud pneys, drawn
towards him with perfect ease, a galley which Law
ION the shore manned and loaded. He also re-
marked "gve me where ] may stand and win
move The world" When Syracuse was beseiged
by The Roman consul Marctllls, il was for a long
time defended by the coDIiVahces Of Archimedes


who's showPred long darts and heavy stones in great
quantities upon the enemy, and often lifted into the
air ships that had come near the walls and letting
them fall dashed to pieces when they removed
beyond the reach Of bis cranes and levers he con-
trived to set Ere to them by means of the rays Of
the sun, reflected from burning glasses. But not
Withstand mg the art of Archipedes,the' CITY was
at length taken by storm. Al the time Archimedes
was go very intent upon solving sope problemthati
he neither heard the noise nor regarded any thing


until being ordered by the Roman soldier follow
him to Marceus, be babe him begone aud not in
terrnpt him by such nonsense as he would go po
where before he had finished his deInoustFation;
the soldier eRraged, struck him dead on the spot


When ndyiDg he requested that sphere, inscribed
in cylinder might be engraved on his tomb 10
petpetaate his noble discovery. Cicero 1876 years
afterwards discovered his monument, overgrown
with thorns and hrsmbes, which he knew only by
the inscription, ignorant and ungratefnl. were
his countryn -. =. FRANKLIN.
~ = For the North Carolina Staadard.


. -FOUR RT4 of IfJI V Z L