Alberti, Leone Battista
,
Architecture
,
1755
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theſe other two in a juſt Relation or proporti
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onate Interval, which Interval is the equal re
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lative Diſtance which this Number ſtands from
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the other two. </
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<
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>Of the three Methods moſt
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approved by the Philoſophers for finding this
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Mean, that which is called the arithmetical is
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the moſt eaſy, and is as follows. </
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<
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>Taking the
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two extreme Numbers, as for Inſtance, eight
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for the greateſt, and four for the leaſt, you add
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them together, which produce twelve, which
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twelve being divided in two equal Parts, gives
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us ſix.
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<
cell
>8</
cell
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<
cell
>4</
cell
>
</
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<
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<
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<
cell
>12</
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</
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<
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<
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<
cell
>6</
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</
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<
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>THIS Number ſix the Arithmeticians ſay, is
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the Mean, which ſtanding between four and
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eight, is at an equal Diſtance from each of
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them.
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<
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>8.</
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<
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>6.</
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<
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>4.</
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<
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>THE next Mean is that which is called the
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Geometrical, and is taken thus. </
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<
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>Let the ſmall
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eſt Number, for Example, four, be multiplied
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by the greateſt, which we ſhall ſuppoſe to be
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nine; the Multiplication will produce 36:
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The Root of which Sum as it is called, or the
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Number of its Side being multiplied by itſelf
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muſt alſo produce 36. The Root therefore
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will be ſix, which multiplied by itſelf is 36,
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and this Number ſix, is the Mean.
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<
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>4 Times 9</
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<
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>36</
cell
>
</
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<
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<
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>6 Times 6</
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>
<
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>36</
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>
</
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<
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>THIS geometrical Mean is very difficult to
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find by Numbers, but it is very clear by Lines;
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but of thoſe it is not my Buſineſs to ſpeak
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here. </
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<
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>The third Mean, which is called the
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Muſical, is ſomewhat more difficult to work
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than the Arithmetical; but, however, may be
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very well performed by Numbers. </
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<
s
>In this the
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Proportion between the leaſt Term and the
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greateſt, muſt be the ſame as the Diſtance be
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tween the leaſt and the Mean, and between the
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Mean and the greateſt, as in the following Ex
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ample. </
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<
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>Of the two given Numbers, let the
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leaſt be thirty, and the greateſt ſixty, which is
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juſt the Double of the other. </
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<
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>I take ſuch
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Numbers as cannot be leſs to be double, and
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theſe are one, for the leaſt, and two, for the
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greateſt, which added together make three. </
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<
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>I
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then divide the whole Interval which was be
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tween the greateſt Number, which was ſixty,
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and the leaſt, which was thirty, into three
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Parts, each of which Parts therefore will be
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ten, and one of theſe three Parts I add to the
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leaſt Number, which will make it forty; and
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this will be the muſical Mean deſired.
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<
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>30</
cell
>
<
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/>
<
cell
>60</
cell
>
</
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>
<
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>
<
cell
>1</
cell
>
<
cell
/>
<
cell
>2</
cell
>
</
row
>
<
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>
<
cell
/>
<
cell
>3</
cell
>
<
cell
/>
</
row
>
<
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>
<
cell
>3</
cell
>
<
cell
/>
<
cell
>30</
cell
>
</
row
>
<
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>
<
cell
/>
<
cell
/>
<
cell
>10</
cell
>
</
row
>
<
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>
<
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/>
<
cell
>30</
cell
>
<
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/>
</
row
>
<
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<
cell
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<
cell
>10</
cell
>
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</
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<
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<
cell
>30</
cell
>
<
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>40</
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>
<
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>60</
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>
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<
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>AND this mean Number forty will be diſ
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tant from the greateſt Number juſt double the
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Interval which the Number of the Mean is
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diſtant from the leaſt Number; and the Con
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dition was, that the greateſt Number ſhould
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bear that Portion to the leaſt. </
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<
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>By the Help of
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theſe Mediocrites the Architects have diſcover
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ed many excellent Things, as well with Rela
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tion to the whole Structure, as to its ſeveral
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Parts; which we have not Time here to par
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ticularize. </
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<
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>But the moſt common Uſe they
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have made of theſe Mediocrities, has been how
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ever for their Elevations.</
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<
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>CHAP. VII.</
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Of the Invention of Columns, their Dimenſions and Collocation.
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<
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>It will not be unpleaſant to conſider ſome
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further Particulars relating to the three
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Sorts of Columns which the Ancients invent
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ed, in three different Points of Time: And it
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is not at all improbable, that they borrowed the
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Proportions of their Columns from that of the
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Members of the human Body. </
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<
s
>Thus they
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found that from one Side of a Man to the
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other was a ſixth Part of his Height, and that
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from the Navel to the Reins was a tenth. </
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<
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>From
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this Obſervation the Interpreters of our ſacred
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Books, are of Opinion, that
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Noah
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's Ark for
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the Flood was built according to the Propor
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tions of the human Body. </
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<
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>By the ſame Pro
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portions we may reaſonably conjecture, that the
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Ancients erected their Columns, making the
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Height in ſome ſix Times, and in others ten
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Times, the Diameter of the Bottom of the </
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