M A T 
which was the foie ir.ftrument of his art, evinced extra¬ 
ordinary (kill, yet, like molt imitators, in feizing If’ 
the groffer part of the art of Goltzius, he let the JJ 
effer.ce efcape. His numerous engravings, how- /I 
ever, have been valued by collectors ; and are 1 
known by the annexed monogram. J| v JL 
MA'THAM (Theodore), the fon and pupil of the 
preceding artift, was born at Haerlem in the year 1600. 
lie travelled into Italy, where he ftndied in the fchool of 
Cornelius Bloemaert, and in conjunction with him, Perfyn, 
Natalis, and other artifts, he engraved the Itatues of the 
Juftinian palace. Pie did not work with the graver only, 
but fomelimes made ufe of the point ; inott of his woiks 
confiIt of portraits, many of which are executed in a man¬ 
ner which does him honour. 
MA'THAM (Adrian), was alfo of Haerlem, related to 
Theodore and James, and born fome time about the be¬ 
ginning of the feventeenth century ; but he was, on the 
whole, inferior to thofe artifts in merit. He worked with 
the graver only, imitating the elder de Ghein, hut was 
always behind him; nor can it be neceffary to dwell on 
his demerits. 
MATHAN', a town of Africa, in the kingdom of Bour- 
nou, called a royal city. Lat. 18.30. N. I0n.z1.40. E. 
MATHAN'AM, a rivulet in the I He of Anglefea, which 
runs into the Irilh fea below Llanbaderick. 
'MATHAN'ON, a port on the fouth-eaft part of the 
ifland of Cuba, between Cape Cruz and Cape Maizi, which 
affords good anchorage for Osips. 
MATHA'Y, a town of France, in the department of 
the Doubs : four miles north-weft of Blamont, and feven 
north of St. Hypolite. 
MATHEMATIC, or Mathematical, adj. \_mathcma- 
ticus, Lat.] Confidered according to the doctrine of the ma¬ 
thematicians—It is as impofiible for an aggregate of finites 
to comprehend or exhauft one infinite, as it is for tire 
greateft number of mathematic points to amount to, or con- 
ititute, a body. Boyle. — I fuppofe all the particles of mat¬ 
ter to be fituated in an exafl and mathemttical evennefs. 
Bentley. 
The Eaft and Weft 
Upon the globe, a mathematic point 
Only divides: thus happinefs and mifery, 
And all extremes, are ltill contiguous. Denham. 
MATHEMATICAL SECT, one of the two leading 
philofophical fetts, which appeared towards the beginning 
of the feventeenth century : this left direfled its re- 
feaches by the principles of Gafltndi, and fought after 
truth by obfervation and experience. The dilciples of 
this fefl denied the pollihility of erefling on the Isafis of 
metaphyfical and abltraft truths a regular and folid fyf- 
tem of philofophy, without the aid of alfiduous obferv.a- 
tion and repeated experiments, which are the moft natu¬ 
ral and effeflual means of philofophical progrefs and im¬ 
provement. The advancement and reputation of this 
.left, and of natural knowledge in general, were much 
owing to the plan of philofophizing propofed by lord 
Bacon, to the eltabliftiment of the Royal Society in Lon¬ 
don, to the genius and induftry of Mr. Boyle, and to the 
unparalleled refearches and difeoveries of fir Ifaac New¬ 
ton. Barrow, Wallis, Locke, and many others, were of 
this fed. The other left of philofophers was the meta¬ 
physical. 
MATHEMAT'ICALLY, adv. According to the laws 
of the mathematical fciences.—We may be mathematically 
certain, that the heat of the fun is according to the den- 
fity of the fun-beams, and is reciprocally proportional to 
the fquare of the diftance from the body of the fun. Bentley. 
M ATHEMATI'CIAN, f. \maikematicus, Lat. J A man 
verfed in the mathematics.—One of the moft eminent ma¬ 
thematicians of the age affured me, that the greateft plea- 
lure he took in reading Virgil was in examining Aineas’s 
voyage by the map. Addijon’s Speflaior. 
MATHEMATICS,^ The fcience which treats of the 
M A T 531 
ratio and comparifon of quantities, 3 nd therefore defined 
“the fcience of ratios.” Some writers call it “ the feienee 
cf quantitiesbut this is inaccurate, fince it is not quan¬ 
tities themfelves which are the fubjeft of mathematical in- 
veftigation, but the ratio that fuch quantities bear to each 
other. 
The term mathematics is derived from the Greek word 
fA?.Qrio-K;, difeipline, fcience; reprefenting with juftnefs 
and precilion the high idea that we ought to form of this 
branch of human knowledge. In faff, mathematics is a 
methodical concatenation of principles, reafonings, and 
conclufions, always accompanied by certainty, as the truth 
is always evident ; an advantage that particularly charae- 
terifes accurate knowledge and the true fciences, with 
which we mull be careful not to aflqciate metaphyfical no¬ 
tions, conjeflures, nor even the Itrongell probabilities. 
The (ubjefls then of mathematics are the comparifons of 
magnitude, as numbers, velocity, diftance, &c. Thus, 
geometry confiders the relative magnitude and extenfiorc 
of bodies ; altronomy, the relative velocities and diltances 
of the planets ; mechanics, the relative powers and force 
of different machines, See. &c. fome determinate quan¬ 
tity being fixed upon in all cafes as a ftandard of meafure. 
Such are the (ubjefls that fall under the contemplation 
of the mathematician ; and, as far as a knowledge of thefe 
may be confidered beneficial to mankind, fo far, at lead, 
the utility of the fcience on which they depend mud be 
admitted. It is not, however, the application of mathe¬ 
matics to the various purpofes of 1’ocif ty that conftitutes 
their particular excellency ; it is their operation upon the 
mind, the vigour they impart to our intellectual faculties, 
and the difeipline which they impofe upon our wander¬ 
ing reafon. 
Mathematics is divided into two kinds, pure and mixed’. 
In pure mathematics magnitude is confidered in the abitrafl 5 
and, as it is founded on the liinplelt notions of quantity, 
the conclufions to which it leads have the fame evidence 
and certainty as the elementary principles from whicli 
thele conclufions are deduced. This branch of mathe¬ 
matics comprehends, 1. Arithmetic, which treats of the 
properties of numbers, z. Geometry, which treats of 
extenfion as endowed with three dimensions, length, 
breaotTi, and thicknefs, without conlidering the phylical 
qualities infeparable from bodies in their natural Hate. 3.. 
Algebra, fometimes called univerfal arithmetic, which 
compares together all kinds of quantities, whatever be 
tbeir value. 4. The direfl and inverfe method of 
Fluxions (called on the continent, the differential and 
integral calculi ), which confider magnitudes as divided 
into two kinds, conllar.t and variable, the variable mag¬ 
nitudes being generated by motion ; and which deter¬ 
mines the value of quantities from the velocities of the 
motions with which they are generated.— Mixed Mathematics 
is the application of pure mathematics to certain elta- 
biifired phyfical principles, and comprehends all the phy- 
iico-mathematical fciences ; namely, 1. Mechanics with 
Hydrostatics ; z. Optics ; 3. Astronomy ; 4. Acou¬ 
stics; 5. Electricity; and 6. Mac-neti-sm. The 
hiltory of thefe various branches of fcience, and of thofe 
who have excelled in them, being given at full length 
under their refpeclive heads, we fhall at prefent direfl the 
attention of the reader to a few general principles and 
remarks, 
“The mathematics,” fays Dr. Barrow, “effectually ex* 
ercife, not vainly delude, nor vexatioufly torment, ftu- 
dious minds with cbfcure fubtilties, but plainly demon- 
llrate every thing within their reach ; draw certain con- 
clulions, inllruft by profitable rules, and unfold pleafant 
queliions. Thefe difciplines alfo inure and corroborate 
the mind to a conftant diligence in ftudy ; they wholly 
deliver 11s from a credulous limplicity, and moft ftrongly 
fortify us againft the vanity of fcepticilin ; they effectu¬ 
ally reltrain us from a rafti prefumption, moft ealily in¬ 
cline us to a due affent, anu perfeflly fubjeft us to the 
government of right reafon.. While the mind isabftradUd 
