M A T
The firft who cultivated Mathematics after the flood, were the Syrians and Qhalieani 5 from whom, the fame Jofephus adds, they were carried by Abraham to the Egyptians; who proved fuch notable Proficients, that A. rijtotle makes no fcruple to fix the firft Rile of Mathema- tics among them. From Egypt, 584 Years before Chrift, they pafs'd into Greece thro the hands of Tbales, who ha- ving learnt Geometry of the Egyptian Priefts, taught it in his own Country. Alter Hales, comes Pythagoras ; who, among other Mathematical Arts, paid a peculiar regard to Arithmetic ; fetching the grcateft part of his Philofophy from Numbers : He was the firit, as Lamms tells us, who abllraSed Geometry from Matter ; and to him we owe the Doctrine of mammenfurMe Magnitudes, and the five regular Bodies, betides the firft Principles ofiVfe- flc and Aftronomy. Pythagoras was fucceeded by Amx- agoras, Oer.opides, Brtftt, AxtyfU, and Hippocrates of Scia ; who all applied themfelves particularly to the Quadrature of the Circle, the Duflicature of the Cube, fjc. but the laft with mod Succefs : This laft is alfo mention'd by Froclus as the firft who compiled Elements of Mathe- matics.
Democritus excelled in Mathematics as well as Phyfics ; tho none of his Works in either kind are extant : the De- duction of which, fotne Authors lay at Arifiotle's door. The next in order is PlaUj who not only improved Geo- metty, but introduced it into Phyfics, and fo laid the Foundation of a folid Philofophy. Out of his School pro- ceeded a Croud of Mathematicians. Proclus mentions thir- teen of Note ; among whom was Leodamus, who improved the Analyfis firft invented by Plato 1 Tbmtetus, who wrote Elements ; and Archytas, who has the Credit of being the firft who applied Mathematics to Ufe in Life. Thefe were fucceeded by Neoclidis and Than, the laft of whom con- tributed to the Elements. Ettdoxus excelled in Arithmetic and Geometry, and was the firft Founder of a Syftem of Ajlronomy. Menechmus invented the Conic Sections, and Tbeodrfius and Hermotimus improved the Elements.
For Arijiotle, his Works are fo ftored Kith Mathematics, that Blancantts compiled a whole Book of them ; Out of his School came Eudemus and Theopbrajius ; the firft of which wrote of Numbers.; Geometry, and indivifible Lines ; the latter a Mathematical Hijiory. To Arijleus Ifidorus, anAHypJicles, we owe the Books of Solids; which,' with the other Books of Elements, were improved, col- lected and methodized by Euclid, who died 284 Years before Chrift. An hundred Years after Euclid, came Era- tojlhenes and Archimedes. Cotemporary with the latter was Conon, a Geometrician and Aftronomer. Soon after came Apollonius Pergxus; whofe Conies are -Ct ill extant. To him are likewife afcribed the 14th and 15th Books of Euclid, which are faid to have been contracted by Hypficies. Hip- farehus and Menelaus wrote on the Sukenfes in a Circle the latter alfo on Spherical Triangles ; on 'which Subjea' we have a Work of Tieodojins: And thefe all, Menelaus excepted, lived before Chrift. A.D. 70, Ptolemy of Alex- andria was born 5 the Prince of Aftronomers, and no mean Geometrician : He was fucceeded by the Philofophcr Plutarch, of whom we have {till extant fome Mathemati- cal Problems. After him came Etttocius, who commented on Archimedes, and occasionally mentions the Inventions of Philo, Diodes, Hicomedes, Spouts, and Heron, on the Dupli- cative of the Cube. To Ctefebius of Alexandria, we owe our Pumps ; and Gcminus, who came foon after, is pre- ferred by Proclus fo Euclid himfelf.
Diophantus of Alexandria was a great Maftcr of Num- bers, and the firft Inventer of Algebra : For others of the Antients, Nicomachus is celebrated for his Arithmetical, Geometrical, and Mufical Works; Serenas for his Books on the SeUion of the Cylinder; Proclus, for his Comments on Euclid; and Theon has the Credit among fome, of be- ing Author of the Books of Elements afcribed to Euclid himfelf. The laft to be named among the Antients, is Pappus of Alexandria, who flourifh'd A. D. 400, and is ce- lebrated for his Books of Mathematical Colle3ious ftill extant.
See the Progrefs of each Branch of Mathematics, with the Authors who have wrote on it, under the refpective Heads; as Geometry, Mechanics, Algeiira, A-
STRONOMY, Ji?C,
Mathematics are diftinguifti'd with regard to their End, into Speculative, which reft in the bare Contem- plation of the Properties of Things; and Practical, which apply the Knowledge ot thofe Properties to fome Ufes in Life.
With regard to their Object, Mathematics are divided info pare or abftrahl ; and mix'd. Pure Mathematics cou- .fider Quantity, abftractedly 5 and without any relation to Matter: Mix'd Mathematics conlider Quantity as fubfift- ing in material Beings, and as continually intetwove.
Pure Mathematics again, either confider Quantity as discrete, and fo compatible, as Arithmetic j or as con-
I W )
MAT
crete, or continued, and fo meafurable, as Geometry and* Ingonometry. See Arithmetic, Geometry, 15c
M.»V Mathematics are very extenftve, and are di- ifinguimd by various Names, as the Subjects they con- lider, and the Views wherein they take them, vary: it being fufficicnt to determine an Art to be a Branch of mix d Mathematics, that pure Mathematics are applicable thereto i.e. that it may be explain'd and demonftrated from the Principles of Arithmetic and Geometry. Such are,
Mechanics, which confider Motion, or the Laws of moving Bodies. See Motion.
Hydrcfiatics, confider the Laws of Fluids, or of Bodies gravitating in Fluids. See Fluid:
Pneumatics, the Air, with regard to the Laws and Meti- furation thereof. See Air.
Hydraulics, the Motion of Fluids; SeeFniim.
Optics, direct Light or Villon. See Vision.
Catoptrics, reflected Virion. See Reflection.
Dioptricsj refracted Virion. See Refraction.
Perfpcllhe, the Images of Objects, in order to delineate or reprefent them. See Perspective.
Ajlronomy, the Univerfe, and the Phenomena of the Heavens. SccFIeavenly Bodies. _ Geography, the Earth, both as in itfelf, and in its Affec- tions. See Earth.
Hydrography, the Sea, principally as navigable. See Navigation.
Chronology, Time, with regard to the meafuring and di- ftinguilhing thereof. See Time, Year, Efocha, £5~c.
Gnomonics, or Dialling ; Shadows, in order for determin- ing the Flour of the Day. See Dial and Shadow.
Pyrotechny, Artificial Fires, with regard both to Diver- "°n, and to the Ufes of War. See Fires. Rockets, (2c.
Military Architecture, the Strength of Places, with regard to their Defence againft an Enemy. See Fortification.
Got/ Architecture (now become a Branch of Mathematics} Buildings. See Building.
Mafic, Sounds, and their Effects on the Ear. See Sound, Tune, iSc
For the Elements of each, fee the refpective Heads. For an accurate Syftem of all the Parts above- mention'd (Mnjk alone excepted) orderly digefted, and clearly de- monftrated, fee the excellent Wolfiuss Elementa Matbefeos Unherjie.
MATHURINE, fee Trinxtarian.
MATINS, the firil part of the daily Service in the Ro- nujh Church- lAatini is fometimes held early in the Morning, fometimes at Midnight, and fometimes the E- ven before. And infirm People, even in Monalteries, are difpenfed from attending Matins. The Word comes from the Trench Math?, Mornings
MATRASS, or Bolt Head, a Veffel of Glafs ufed by the Chymills in Diftillation, and other Operations. It is made in form of a Bottle, with a very long narrow Neck. The Matfafs is luted with Earth, when it is to be placed on a very hot Fire. When 'tis tcrjuired it /houlcl be iropped very clofe, they feal it hermetically. The Word comes originally from the Language of the antient Gauls. See Bolt-Head.
MATRICE, fee Matrix.
Matrice, in Dying, is applied to the five fimple Co- lours, whence all the reft are derived or compofed. Thefe are the Black, White, Blue, Red, and Fallow or Root Colour. See Colours.
Matrices, ufed by the Letter-Founders, are thofe little Pieces of Copper or Brals, at one end whereof are engraven, dent-wife, or en crexx, the feveral Characters ufed in the Compoiing of Books. Each Character, Vir^ula^ and even Point, in a Difcourfe, has its feveral Matties, and of confi.quence its feveral Puncheon to ftrike it. "lis tie Engravers on Metal that cut or grave the Matrices : See Engraving. When any Types are to be caft, the Ma- trice is fallen'd to the End of a Mould, fo difpofed, as that when the Metal is thrown on it, it may fall into the Cteux or Cavity of the Matrice, and take the Figure and Impreffion thereof. See Letter Foundery. See alfo Type, and Printing.
The Matrices ufed 'hi Coining are Pieces of Steel iri form of Dyes ; whereon are engraven the feveral Figures, Arms, Characters, Legends, <i$c. wherewith the Species are to be llamp'd. The Engraving isperform'd with fe- veral Puncheons, which being form'd in relievo, or pro- minent i when (truck on the Meta], make an indented Imprcflion, which the French call en creux ; and for which^ I don't know we have any precife Name at all. See the Manner hereof under Engraving on Steel. See alfo Co 1 n 1 n g .
MATRICULA, a Regiller kept of the Admiflion of
Officers, and Perfons entcr'd into any Body or Society,
whereof a Lift is made. .Among Ecclefiaftical Authors^
we find mention made of two Kinds of Matrictih's : the one
O o o o eon^
