ced for the Proof of any one Problems or Thearem, the formen don't always depend of the latter, get it don't readily enough appear either from the order of cach, or by any other manner, when they agree together, and when not"; wherefore for want of tbe Conjunctions and Adjectives, ergo, rursus, orci many difficulties and occaftons of doubt do ofron arise in reading, especially to those that are Novices. Besides it frequently beppëns, that the said Method cannot avoid Superfinous Repetitions, by which the Demonstrations are oftentimes render'd tedious, and sometimes also more intriz cate ; wbich Faults any Method doth easily remedy by my

bja the arbitrary mixture of both Words and Signs. There fore let what bas been said, touching the Intention and Method of this little Work, Suffice. As to the reft, whoever cavets to please himself with what

mage be faid, either in Praise of the Mathematicks in general, or of Geometry in particular, or touching the His story of these Sciences, and consequently of Euclide himself, (who digested those Elements) and others Eu terms of that kind, may confule other Interpreters: Neither' will I (as if I-were afraid least

: thefe my Endeavors may fall short of being fatisfačtary to all Pera jons) alledge as an Exeuse (ibo' I may very Lawfully do it) the want of due time which onght to be em ploy'd in this Work, nor the Interruption occafran'd by other Affairs, nor yet the want of requifica belp for these Studies nor several 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 wbolig submit to bis' Cenfure and Judgment, to approve if useful, or reje&t if otherwise.

J. B.

contracto, Euangelouós.

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Senex profundus, & aphorismos iudwit.
Immensa dudum margo commentarii
Diagramma circuit minutum , utque Insuli
Problema breve natabat in vasto mari.
Sed unda jam detumuit; & glofa ar&ior
Stringit Theoremata : minoris anguli
Lateribus ecce totus Euclides jatet,
Inclusus olim velut Homerus in nuce;
Pluteoque sarcina modo qui intubait, levis
En fit manipulus. Pelle in exigua latet
Ingens Maibelis, måtris utero Hercules,
In glande quercus, vel Ithaca Eurus ir pila,
Nec mole duni decrescit, ufu fit minor
Quin auctior jam evadit, & cumulatius
Contra&ta prodeft erudita pagina,
Sic ubere magis liquor è preffo afluit;
Sic pleniori vafa inundat

Torrente cordis Syftole; fic fuftus
Procurrit &quor ex Abyla angustiis.
Tantilli operis ars 'tants tenda wire eft
BAROVIANO nomini, ac folertia.
Sublimis euge mentis ingentium potens !
Cui invitun nil, arduum effe nil solet;
Sic usque pergas profpero conamine,
Radiufque multumi debeat ac abacus tibi ;
Sic crefcat indies feracior seges,
Simili colonum germinc ashtuo beans.
Specimen future meflis hic fiet labor.
Magnaque faina illuftria hac preludia.
Juvenis dedit qui tauta, quid dabit fenex ?

C. Robotnam, CMNTS,

Col. Erin. Sen. Soc.



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More, or to be added.

Less, or to be subtracted.


The Differences, or Excels; Also, that all

the quantities which follow, are to be

subtracted, the signs not being changed.
Multiplication, of the Drawing one side of

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

of letters; as AB = AX 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 squarc


Other Abbreviations of words, where ever they accur, the Reader will without trouble underft and of

, bimself ; Saving Some few, which, being of less general nfé, we refer to be explained in their places. ca


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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.

VIll. A plain Angle is the inclination of two lines the one to the other, the one touching the other in ihe 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 equalangles 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 beweth 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 AGC.

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

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

right angle; as ACB. B.

D XIII. Å 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. c

XVII. A Diameter of a E

circle is a right line drawn through the center there

of, and ending at the cirD cumference on either fide,

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