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ced for the Proof of any one Problems or Thearem, the former-don't always depend of the latter, get it don't readily enough appear either from the order of each, an by any other manner, when they agree together, and when not; wherefore for want of the Conjunctions and Adjectives, ergo, rursus, e-ci many difficulties anch occaftons of doubt do often arise in reading, especially to those that are Novices

. Besides it frequently heppens, that the faid Method cannot avoid fuperfinous Repetitions, by which the Demonstrations are often times renderà tedious, and sometimes alfo more intria caté; which Faults my Method doth easily remedy by the arbitrary mixture of both Words and Signs. There fore let what bas been said, touching the Intention and Method of this little Work, fuffice. As to the reft, whoever cavets to please himself with wbat may be faid, either in Praise of the Mathematicks in general, or of Geometry in particular, or touching the Him story of these Sciences, and consequently of Euclide himself, who digested those Elements) and others Ecotoring of that kind, may confult other Interpreters: Neither will I (as if I were afraid leaf these my Endeavors may fall short of being fatisfactory to all Pere Jons) alledge as an Exeuse (tbo? I may very lawfully do it) the want of due time which ought to be ema ploy'd in this work, nor the Interruption occafian'd by biher Affairs, nor yet the want of réquisite belp for tbefe Studies nor feveral other things of the like nature But what I have bere employ'd my Labour and Study in for the Use of the ingenuous Reader, I wholly fubmit to bis Censure and Fudgment, so approve if Hefulor reject if otherwijë.

J. B.

contracto, Euangeloués.

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A&um bene ! didicit Laconice loqui

Senex profundus, & aphorismos induit.
Immensa du&um margo commentarii
Diagramma circuit minutum , utque Insula
Problema breve natabat in vasto nari.
Sed unda jam detumuit; & glofa ar&tior
Stringit Theoremata : minoris

anguli
Lateribus ecce totus Euclides jatet,
Inclusus olim velut Homerus in nuce;
Pluteoque Jarcina modo q«i«intubait, levis

En fit manipulus, Pelle in exigua latet
Ingens Matbelis, matris utero Hercules,
In glande quercus, vel Ithaca 'Eurus in pila,
Nec mole duni decrefcit, ufi ftt minor
Quin auctior jam evadit, & cumulatius
Contra&ta prodeft erudita pagina,
Sic ubere magis liquor è preffo affluit;
Sic pleniori vasa inundat

fanguinis
Torrente cordis Systole.; kc fuftus
Procurrit aquor er Abyla angustiis.
Tantili operis ars 'tanta referenda unire eft
BAROVIANO nomini, ac folertia.!
Sublimis euge mentis ingentium potens !
Cui invitum nil, arduum efle nil solet ;
Sic usque pergas prospero conamine,
Radiusque multumi debeat ac abacus tibi;
Sic crefcat indies feracior seges,
Simili colonum germinc asiduo beans.
Specimen futuræ mefis hic fiet labor.
Magnaque famæ illuftria hac praldia.
Juvenis dedit qui tauta, quid dabit fenex ?

Car. Robotham, CANTAB.

Coll. Trin, Sen. Soc.

The

Characters.

r Equal,

Greater,

Leffer.

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More, or to be added.

Less, or to be subtracted.

Signifies

The Differences, or Excels; Also, that all

the quantities which follow, are to be

subtra&ted, the signs not being changed. Multiplication, or the Drawing one side of

a Rectangle into another.
The same is denoted by the Conjunction

of letters; as ABAX B.
The Side or Root of a Square, or Cube, &C.
A Square.

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A Cube.

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The ratio of a square "number to a square

number.

Other Abbreviations of words, where ever they accur, the Reader will without trouble understand of kimself ; Saving some few, which, being of less general wife, we refer to be explained in their places.

.The

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A

Definitions.
I.

Point is that which has no part.

II. A Line is a longitude without latitude.

III. The ends, or limits, of a

line are Points. IV. A Right Line is that which lies equally betwixt its Points.

V. A Superficies is that which has only longitude and latitude,

VI. The extremes, or limits, of a Superficies are lines.

VII. A plain Superficies is that which lies equally betwixt its lines.

VIH. A plain Angle is the inclination of two lines the one to the other, the one touching the other in the same plain, yet not lying in the same strait line.

IX. And if the lines which contain the Angle be right lines, it is called a right-lined Angle.

X, When

X. When a right line CG ftanding upon a right line AB, makes the angles on either side thereof,

CGA, CGB, equal one B to the other, then both

those equal angles are right

angles ; and the right line CG, which standeth on the other, is termed a Perpendicular to that (AB) whereon it ftandeth,

Note, When several angles meet at the same point (as at G) each particular

angle is described by three letters; whereof the middle letter seweth the angular point, and the two other letters the lines that make that angle : As the angle which the right lines CG, AG make at G, is called CGA, Or AĞC. A

XI. An obtufe angle is that which is greater than a right angle ; as ACD.

Xil. An acute angle is that which is less than a

right angle; as ACB. B

D XIII. A Limit, or Term,

is the end of any thing. ': XIV. A Figure is that which is contained under one or more terms.

XV. A Circle is a plain figure contained under one line, which is called a Circumference ; unto which all lines drawn from one point within the figure, and falling upon the circumference thereof, are equal the one to the other. B

XVI. And that point is called the Center of the

Circle. A

C

XVII. A Diameter of a circle is a right line drawn through the center thereof, and ending at the circumference on either fide,

divi

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