按键盘上方向键 ← 或 → 可快速上下翻页，按键盘上的 Enter 键可回到本书目录页，按键盘上方向键 ↑ 可回到本页顶部！
————未阅读完？加入书签已便下次继续阅读！
not as an enemy； but as a friend。 Now； the one which we maintain to be
the most beautiful of all the many triangles （and we need not speak of
the others） is that of which the double forms a third triangle which
is equilateral； the reason of this would be long to tell； he who
disproves what we are saying； and shows that we are mistaken； may
claim a friendly victory。 Then let us choose two triangles； out of
which fire and the other elements have been constructed； one
isosceles； the other having the square of the longer side equal to
three times the square of the lesser side。
Now is the time to explain what was before obscurely said： there was
an error in imagining that all the four elements might be generated by
and into one another； this； I say； was an erroneous supposition； for
there are generated from the triangles which we have selected four
kinds…three from the one which has the sides unequal； the fourth alone
is framed out of the isosceles triangle。 Hence they cannot all be
resolved into one another； a great number of small bodies being
combined into a few large ones； or the converse。 But three of them can
be thus resolved and compounded； for they all spring from one； and
when the greater bodies are broken up； many small bodies will spring
up out of them and take their own proper figures； or； again； when many
small bodies are dissolved into their triangles； if they become one；
they will form one large mass of another kind。 So much for their
passage into one another。 I have now to speak of their several
kinds； and show out of what combinations of numbers each of them was
formed。 The first will be the simplest and smallest construction；
and its element is that triangle which has its hypotenuse twice the
lesser side。 When two such triangles are joined at the diagonal； and
this is repeated three times； and the triangles rest their diagonals
and shorter sides on the same point as a centre； a single
equilateral triangle is formed out of six triangles； and four
equilateral triangles； if put together； make out of every three
plane angles one solid angle； being that which is nearest to the
most obtuse of plane angles； and out of the combination of these
four angles arises the first solid form which distributes into equal
and similar parts the whole circle in which it is inscribed。 The
second species of solid is formed out of the same triangles； which
unite as eight equilateral triangles and form one solid angle out of
four plane angles； and out of six such angles the second body is
completed。 And the third body is made up of 120 triangular elements；
forming twelve solid angles； each of them included in five plane
equilateral triangles； having altogether twenty bases； each of which
is an equilateral triangle。 The one element ＇that is； the triangle
which has its hypotenuse twice the lesser side＇ having generated these
figures； generated no more； but the isosceles triangle produced the
fourth elementary figure； which is compounded of four such
triangles； joining their right angles in a centre； and forming one
equilateral quadrangle。 Six of these united form eight solid angles；
each of which is made by the combination of three plane right
angles； the figure of the body thus composed is a cube； having six
plane quadrangular equilateral bases。 There was yet a fifth
combination which God used in the delineation of the universe。
Now； he who； duly reflecting on all this； enquires whether the
worlds are to be regarded as indefinite or definite in number； will be
of opinion that the notion of their indefiniteness is characteristic
of a sadly indefinite and ignorant mind。 He； however； who raises the
question whether they are to be truly regarded as one or five； takes
up a more reasonable position。 Arguing from probabilities； I am of
opinion that they are one； another； regarding the question from
another point of view； will be of another mind。 But； leaving this
enquiry； let us proceed to distribute the elementary forms； which have
now been created in idea； among the four elements。
To earth； then； let us assign the cubical form； for earth is the
most immoveable of the four and the most plastic of all bodies； and
that which has the most stable bases must of necessity be of such a
nature。 Now； of the triangles which we assumed at first； that which
has two equal sides is by nature more firmly based than that which has
unequal sides； and of the compound figures which are formed out of
either； the plane equilateral quadrangle has necessarily； a more
stable basis than the equilateral triangle； both in the whole and in
the parts。 Wherefore； in assigning this figure to earth； we adhere
to probability； and to water we assign that one of the remaining forms
which is the least moveable； and the most moveable of them to fire；
and to air that which is intermediate。 Also we assign the smallest
body to fire； and the greatest to water； and the intermediate in
size to air； and； again； the acutest body to fire； and the next in
acuteness to； air； and the third to water。 Of all these elements； that
which has the fewest bases must necessarily be the most moveable；
for it must be the acutest and most penetrating in every way； and also
the lightest as being composed of the smallest number of similar
particles： and the second body has similar properties in a second
degree； and the third body in the third degree。 Let it be agreed；
then； both according to strict reason and according to probability；
that the pyramid is the solid which is the original element and seed
of fire； and let us assign the element which was next in the order
of generation to air； and the third to water。 We must imagine all
these to be so small that no single particle of any of the four
kinds is seen by us on account of their smallness： but when many of
them are collected together their aggregates are seen。 And the
ratios of their numbers； motions； and other properties； everywhere
God； as far as necessity allowed or gave consent； has exactly
perfected； and harmonised in due proportion。
From all that we have just been saying about the elements or
kinds； the most probable conclusion is as follows：…earth； when meeting
with fire and dissolved by its sharpness； whether the dissolution take
place in the fire itself or perhaps in some mass of air or water； is
borne hither and thither； until its parts； meeting together and
mutually harmonising； again become earth； for they can never take
any other form。 But water； when divided by fire or by air； on
reforming； may become one part fire and two parts air； and a single
volume of air divided becomes two of fire。 Again； when a small body of
fire is contained in a larger body of air or water or earth； and
both are moving； and the fire struggling is overcome and broken up；
then two volumes of fire form one volume of air； and when air is
overcome and cut up into small pieces； two and a half parts of air are
condensed into one part of water。 Let us consider the matter in
another way。 When one of the other elements is fastened upon by
fire； and is cut by