DEM

238

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that of a circle, whereby it is said to beon . ~y the motion of a right line round a fixed point ;niti otl ^ 0 °ting, what was before instanced as a real defi-This a circle, amounts to no more than a nominal one.aff 0r( j a ^ct'on of a real definition is very strict and just; andone, -p su fficient distinction between a real and a nominalOes 3i though it has the advantages of analogy, distinct-^tt'inal , Con y en i ence ) on its side; yet being only itself anitio n ae ® n ition, i. e., a definition of the term real defi-tra r ji ’ T 6 rnust consider it in the light of an idea fixed arbi-that ^ at tvord, and which Wolfius always denotes by

to ot her “ enumerated in a definition, some are commonther eto . lln S s beside the thing defined ; others are peculiarSecond j; t le first are called the genus, or kind; and thecircle, i di fference. Thus, in the former definition of a^* s tat»t fr a ?^ ure whose circumference is everywhere equi-tiatn e Co ° m lts centre ; the word figure is the kind, as being atest tl le to all other figures, as well as to the circle ; thefrom ev 'ficrence, which specifies or distinguishes this figurefrr t] le other. And hence arises that rule of F. de Colonia,that J s a hing of a definition. “ Take,” says he, “ somethingto j t Coin,no n to the thing defined with other things, andg enua ome tbing that is proper, or peculiar to it; i. e., join?*t>on,” snd specific difference, and you will have a defi-*• A deg • . s P e cial rules for a good definition are these:—?8ree to ni . tlon must be universal or adequate, that is, it must!?clnd e ,j al the particular species, or individuals, that arcto tl 1 Ur ',® r the same idea. 2. It must be proper, and pecu-r,1 frs beini! lln ^ ^ e fi ne< ^> an d agree to that alone. These twof'toeal witl? ?fr serv ed, will always render a definition reel-ed ; n , the thing defined, that is, the definition may beTotally m P' ace the thing defined ; or they may be® h °uld b e | rrnei ^ concerning each other. 3. A definitionw^in* an< ^ P^ a ' n > an( l) indeed, it is a general rulei sboij]?? 6 definition both of names and things, that no„? it, Un j e he used in either of them which has any difficultys 11 has been before defined. 4. A definitionor t, so that it must have no tautology in it, nord R ler e sy Su P er fluous. 5. Neither the thing defined, nor^I’fr'on ^ non ym°us name, should make any part of the

«EFt'

1 Word • , “““ "

Of ^ u ln the course of his book,

- y ^ords

It

carve^ CTI °N, a term applied to the distance by which’ 8 u Se( i'I >a ^ 8 from a straight line, or from another curve.TCtion - ere

both decline and

. .,„ n . re any “ bending off” takes place; the word

in , -'INott-II 10 *'’ means “ bending off.”

or ?? ING MALS, such asIffir recli ne

St

of Con ~ VJA>1 , in Roman antiquity, a temple with a large!pj e s ® crat ed ground round it. Also that portionln which the altar or idol was placed. See

a term applied to that class of sculp-he figures are raised only halfway above thefirieti •^OlSTSTl? a

filmed of ,, NATION, (from the Latin ) in mathematics, a' s air'* V tw SOnin - whereby the truth of an assertion isestni i-° r a ser * es °f propositions, whose truth

fi'e 4*7/1

1 | ( 8tl 'at es 111 Proposition of the first book of Euclidtr U e . 9 8u Ppositj Certa * n property of a right-angled triangle,Cr ’ that th n ’~Tl’ that all the preceding propositions arefria „„ !*d, ar e t ax *°ms used in geometry, whether expressed

of

th e ’ n’ 6 true also. It makes the consequence as cer-O® coan emises > b y means of the indubitable character^strati‘® ctl ng Process. This strict use of the termfrclongs to the

science of logic,3 o

which is the

art of demonstrating from premises, without reference to thetruth or falsehood of the premises themselves. In effect, Ithe demonstrations of mathematicians are no other thanseries of entliymemes; everything is concluded by force ofsyllogism, only omitting the premises, which either occurof their own accord, or are recollected by means of quota-tions. To have the demonstration perfect, the premises ofthe syllogisms should be proved by new syllogisms, till at Ilength you arrive at a syllogism, wherein the premises areeither definitions, or identical propositions.

Indeed, it might be demonstrated, that there cannot be agenuine demonstration, i. e., such a one as shall give full con-viction, unless the thoughts be directed therein according tothe rules of syllogism. Clavius, it is well known, resolvedthe demonstration of the first proposition of Euclid intosyllogism : Herlinus and Dasipodius demonstrated the wholesix first books of Euclid , and Henischus, all arithmetic, inthe syllogistic form.

Yet the generality of persons, and sometimes even mathe-maticians, imagine, that mathematical demonstrations are con-ducted in a manner far remote from the laws of syllogism ; sofar are they from allowing that those derive all their forceand conviction from these. But men of the greatest abilityhave taken our view of the question. M. Leibnitz, forinstance, declares that demonstration to be firm and valid,which is in the form prescribed by logic ; and Dr. Wallisconfesses, that what is proposed to be proved in mathematics jis deduced by means of one or more syllogisms : the great iHuygens, too, observes, that paralogisms frequently happenin mathematics, through want of observing the syllogistic 1form. i

Problems consist of three parts : a proposition, resolution, I

and demonstration. I

In the proposition is indicated the thing to be done. 1

In the resolution, the several steps are orderly rehearsed,whereby the thing proposed is performed. j

Lastly, in the demonstration, it is shown, that the things jenjoined by the resolution being done, that which was requiredin the proposition is effected. As often, therefore, as a pro- I

blem is to be demonstrated, it is converted into a theorem ; |

the resolution being the hypothesis, and the proposition thethesis: for the general tenor of all problems to be demon-strated is this ; that the thing prescribed in the resolution 1being performed, the thing required is done. i

The schoolmen make two kinds of demonstration : the one ,

ns Sion, or propter quod; wherein an effect is proved by the j

next cause : as when it is proved, that the moon is eclipsed i

because the earth is then between the sun and moon. Thesecond, ns on, or quia ; wherein the cause is proved froma remote effect: as when it is proved that fire is hot, becauseit burns ; or that plants do not breathe, because they are not j

animals ; or that there is a God , from the works of creation. !

The former is called demonstration a priori, and the latterdemonstration a posteriori.

Demonstration, Geometrical, is that framed of reasonings 1drawn from the elements of geometry.

Demonstration, Mechanical, is that, the reasoningswhereof are drawn from the rules of mechanics.

DENDERAH, the Tentyra of the ancients, a ruinedtown of Upper Egypt , celebrated for its temple, which isone of the most splendid remains of antiquity in all Egypt .

Dr. Richardson, Belzoni, and others, have given descriptionsof this temple, which the first-named traveller considers tohave been erected in the period of the Ptolemies . Its remains i \occupy a vast extent of ground, and consist of various build- j iings, besides the temple itself. These are enclosed within j

a wall built of sun-dried bricks, in some places 35 feet high, !