GEO 
nmfcles, and vcfTels of the body are contrived mod 
TCrfr/ca//v,according to the llridteft rules of meclianics./Jay. 
GEOMETRI'CIAN, f. iysutf/.e-pr.^.} One Ikilled in 
geometry ; a geometer.—How ealily does an expert gco- 
mctn'a'an, witli one glance of Itis eye, take in a compli¬ 
cated diagram, made up of many lines and circles ! IVatts. 
To GE'O'METRIZE, V, a. [ysw/xsTfEW.] To fafhion or 
form according to the laws of geometry.—We obtained 
good {lore of cryftals, wliole figures were differing 
enougli, though prettily fltaped, as if nature had at once 
affefted variety in their figuration, and yet confined her- 
Self to q-eomel/ize. Boyle. 
GEO'iMETRY, /'. \_geometric, Fr. geometria, Lat. yio- 
Gr. of yri, the earth, and to meafure.] 
Tlie art of mealuring the earth, and of determining any 
diffances or dimenfions contained within it; and it is alfo 
iifed to denote th.e fcience of local extenlion, quantity, 
or magnitude, abftradtedly confidered, without any re¬ 
gard to matter. Hence to this fcience might be referred 
the coniideration not only of lines, furfaces, and folids; 
but alfo of time, velocity, number, weight, &:c. infomuch 
that tvith tile aid of arithmetic or algebra, geometry now 
forms the chief foundation of the mathematics. 
Herodotus, Diodorus, Strabo, and Procius, aferibe the 
invention of geometry to the Egyptians, and affert that 
the annual inundations of the Nile gave occafion to it; 
for thole waters bearing away the bounds and land-marks 
of ellates and farms, covering the face of the ground uni¬ 
formly with mud, the people, fay they, were obliged 
every year to diltinguifli and lay out their lands by the 
confideration of their figure and quantity; and thus by 
experience and habit they formed a method or art, which 
was the origin of geometry. A farther contemplation 
of the draughts of figures of fields thus laid down, and 
plotted in proportion, might naturally lead them to the 
difcover,y of loine of their excellent and wonderful pro¬ 
perties; which fpeculation continually improving, tlie 
art continually gained ground, and made advances more 
and more towards perfection. Jofephus, however, feems 
to aferibe the invention to the Hebrews: and others of 
the ancients make Mercury the inventor. Polyd. Virgil, de 
Invent. Per. ill), i, cap. i8. 
From Egypt this fcience pafTed into Greece, being 
carried thither by 'I'hales ; where it was much cultivated 
and improved by himf'elf, as alfo by Pythagoras, Anaxa¬ 
goras of Clazomene, Hippocrates of Chios, and Plato, 
who teltilied his conviction of the neceflity and import¬ 
ance of geometry to the fuccefsful ftudy of philol'ophy, 
by this infeription over the door of his academy. Let no 
me ignorant of geometry enter here. Plato thought the word 
geometry too limited a term for this fcience, and fubfii- 
tuted inftead of it the more extenfive name of Menfuration ; 
and after him others gave U the title of Pantometry. But 
thefe are now become too fcanty in their import, fully 
to comprehend its extent; for it not only inquires into, 
and demonftrates, the quantities of magnitudes, but alfo 
their qualities, as the fpecies, figures, ratios, pofitions, 
transformations, defci iptions, divifions, the finding of 
their centres, diameters, tangents, afymptotes, curvature, 
&c. Some again define it as the fcience of inquiring, 
inventing, and demonflrating, all the affeCfions of mag¬ 
nitude. And Procius calls it the knowledge of magni¬ 
tudes and figures, with their limitations ; as alfo of their 
ratios, affections, pofitions, and motions of.every kind. 
About fifty years after Plato, lived Euclid, who col- 
ledled together all tliofe theorems which had been in¬ 
vented by his predeceffors in Egypt and Greece, and di- 
gefted them into fifteen books, called the “ Elements of 
Geometry demonlfrating and arranging the whole in 
a very accurate and pertedt manner. The next to Euclid, 
of thofe ancient writers whofe works are extant, is Apoi- 
lonius Pergreus, who flourifhed in the time of Ptolemy 
Eiuergetes, about two hundred and thirty years before 
Chrift, and about one hundred years after Euclid. He 
was author of the firft and principal work on Conic 
VoL. VlII. No. 513. 
GEO 417 
Sedlions ; on account of which, and liis other accurate 
and ingenious geometrical writings, he acquired from 
his patron the emphatical appellation of The Great Geome¬ 
trician. Contemporary w'ith Apollonius, or perliaps a 
few years before him, flourifhed Archimedes, Celebrated 
for his mechanical inventions at the fiege of Syracufe, 
and not lei’s fo for his very many ingenious geometrical 
compofitions. 
We can only mention Eudoxus of Cnydus, Archytas 
of Tarentum, Philolaus, Eraloffliene.-;, Ariftarchus of 
Samos, Dinoftratus, the inventor of the quadratrix, Me- 
nechmus, his.brother, and thedifciple of Plato, the two 
Arii'teus’s,Conon,Thracidius,Nicoteles,Leon,'ri)eudius, 
Flermotimus, Hero, and Nicomedes, the inventor of the 
conchoid : befides wliom, there are many other ancient 
geometricians, to whom this fcience has been indebted. 
The Greeks continued their attention to it, even after 
tliey were fubdued by the Romans. Where.is tlie Ro¬ 
mans themfelveswere fo little acquainted with it, even 
in the rr<oft flourifliing time of their republic, tliat Ta¬ 
citus informs us they gave the name of matliematicians 
to thofe who purfued the chimeras of divination and 
judicial aflrology. Nor does it appear they were more 
ciifpol'cd to cultivate geometry during the decline, and 
after the fall, of tlie Roman empire. But the cafe was 
different with the Greeks ; among Vvliom arc found many 
excellent geometricians fince the commencement of the 
Chriflian era, and after the tranflation of the Roman em¬ 
pire. Ptolemy lived under Marcus Aurelius; and we 
have /fill extant the W'orks of Pappus of Alexandria, 
who lived in the time of Theodofius; the commentary 
of Eutocius the Afcalonite, who lived about the year 
of Chrift 540, on Archimedes’s menfuration of the cir. 
cle ; and the commentary on Euclid, by Procius, who 
lived under the empire of Anaffafuis. 
The confequent inundation of ignorance and barbarirm 
was unfavourable to geometry, as w'cll as to tjie other 
fciences ; and the few who applied themfelves to this 
fcience, were calumniated as magicians. However, in 
tliofe times of European darknefs, the Arabians were 
diflinguiflied as the guardians and promoters of fcience ; 
and from the ninth to the fourteenth century, they pro¬ 
duced many affronoiners, geometricians, geographers, 
&:c. from whom the mathematical fciences were again 
received into Spain, Italy, and tlie red of Europe, fome- 
what before the year 1400. Some of the earliell writers 
after this period are, Leonardos Pifanus, Lucas Paciolus 
or De Burgo, and others between 1400 and 1500. And 
after this appeared many editions of Euclid, or commen¬ 
taries upon him: thus, Orontius Finasus, in 1530, pub- 
liflied a commentary on the firft fix books; as did James 
Peletarius, in 1557 ; and about the fame time Nicholas 
Tartaglia publilhed a commentary on the whole fifteen 
bookL There have been alfo the editions, or commen¬ 
taries, of Commandiiie, Clavius, Billingdy, Scheubelius, 
Herlinus, Dafypoclius, Ramus, Herigon, Steviniis, Sa- 
ville, Barrow, Taquet, Dechales, Furnier, Scarborough, 
Kcill, Stone, and many others; but the completell edi¬ 
tion of all tlie works of Euclid, is tliat of Dr. Gregory, 
printed at Oxford 1703, in Greek and Latin : the edition 
of Euclid by Dr. Robert Simfon of Glafgow, containing 
the firft fix books, with the eleventh and twelfth, is much 
efteemetl for its correCtnefs. The principal other elemen¬ 
tary writers, befides the editors of Euclid, are, Borelii, 
Pardies, Marchetti, Wolfius, Simpfon, 6 cc. And among 
thofe who have gene beyond Euclid in the nature of the 
elementary parts of geometry, may be chiefly reckoned, 
Apollonius, in his Conics, his Loci Plani, De Sedtione 
Detenninata, his Tangencies, Inclinatjons, Seftion of a 
Ratio, Section of a Space, &c. ; Arcliifncdes, in his 
treatifes of the Sphere and Cylinder, the Dimenfion of 
the Circle, of Conoids and Spheroids, of Spirals, and 
the Quadrature of the Parabola; Theodofius, in liis 
Spherics; Serenius; in his Sefitions of the Cone and Cy- 
Under ; Kepler’s Nova Stercometria ; Cavalerius’s Geo- 
5 O ■ - nietria 
