the&longs;e other two in a ju&longs;t Relation or proporti<lb/>
onate Interval, which Interval is the equal re<lb/>
lative Di&longs;tance which this Number &longs;tands from <lb/>
the other two. </s> <s>Of the three Methods mo&longs;t <lb/>
approved by the Philo&longs;ophers for finding this <lb/>
Mean, that which is called the arithmetical is <lb/>
the mo&longs;t ea&longs;y, and is as follows. </s> <s>Taking the <lb/>
two extreme Numbers, as for In&longs;tance, eight <lb/>
for the greate&longs;t, and four for the lea&longs;t, you add <lb/>
them together, which produce twelve, which <lb/>
twelve being divided in two equal Parts, gives <lb/>
us &longs;ix.<lb/>
<arrow.to.target n="table16"/></s></p>

<table><table.target id="table16"/><row><cell>8</cell><cell/><cell>4</cell></row><row><cell/><cell>12</cell><cell/></row><row><cell/><cell>6</cell><cell/></row></table><p type="main"> <s>THIS Number &longs;ix the Arithmeticians &longs;ay, is <lb/>
the Mean, which &longs;tanding between four and <lb/>
eight, is at an equal Di&longs;tance from each of <lb/>
them.<lb/>
<arrow.to.target n="table17"/></s></p>

<table><table.target id="table17"/><row><cell>8.</cell><cell>6.</cell><cell>4.</cell></row></table><p type="main"> <s>THE next Mean is that which is called the <lb/>
Geometrical, and is taken thus. </s> <s>Let the &longs;mall<lb/>
e&longs;t Number, for Example, four, be multiplied <lb/>
by the greate&longs;t, which we &longs;hall &longs;uppo&longs;e to be <lb/>
nine; the Multiplication will produce 36: <lb/>
The Root of which Sum as it is called, or the <lb/>
Number of its Side being multiplied by it&longs;elf <lb/>
mu&longs;t al&longs;o produce 36. The Root therefore <lb/>
will be &longs;ix, which multiplied by it&longs;elf is 36, <lb/>
and this Number &longs;ix, is the Mean.<lb/>
<arrow.to.target n="table18"/></s></p>

<table><table.target id="table18"/><row><cell>4 Times 9</cell><cell>36</cell></row><row><cell>6 Times 6</cell><cell>36</cell></row></table><p type="main"> <s>THIS geometrical Mean is very difficult to <lb/>
find by Numbers, but it is very clear by Lines; <lb/>
but of tho&longs;e it is not my Bu&longs;ine&longs;s to &longs;peak <lb/>
here. </s> <s>The third Mean, which is called the <lb/>
Mu&longs;ical, is &longs;omewhat more difficult to work <lb/>
than the Arithmetical; but, however, may be <lb/>
very well performed by Numbers. </s> <s>In this the <lb/>
Proportion between the lea&longs;t Term and the <lb/>
greate&longs;t, mu&longs;t be the &longs;ame as the Di&longs;tance be<lb/>
tween the lea&longs;t and the Mean, and between the <lb/>
Mean and the greate&longs;t, as in the following Ex<lb/>
ample. </s> <s>Of the two given Numbers, let the <lb/>
lea&longs;t be thirty, and the greate&longs;t &longs;ixty, which is <lb/>
ju&longs;t the Double of the other. </s> <s>I take &longs;uch <lb/>
Numbers as cannot be le&longs;s to be double, and <lb/>
the&longs;e are one, for the lea&longs;t, and two, for the <lb/>
greate&longs;t, which added together make three. </s> <s>I <lb/>
then divide the whole Interval which was be<lb/>
tween the greate&longs;t Number, which was &longs;ixty, <lb/>
and the lea&longs;t, which was thirty, into three <lb/>
Parts, each of which Parts therefore will be <lb/>
ten, and one of the&longs;e three Parts I add to the <lb/>
lea&longs;t Number, which will make it forty; and <lb/>
this will be the mu&longs;ical Mean de&longs;ired.<lb/>
<arrow.to.target n="table19"/></s></p>

<table><table.target id="table19"/><row><cell>30</cell><cell/><cell>60</cell></row><row><cell>1</cell><cell/><cell>2</cell></row><row><cell/><cell>3</cell><cell/></row><row><cell>3</cell><cell/><cell>30</cell></row><row><cell/><cell/><cell>10</cell></row><row><cell/><cell>30</cell><cell/></row><row><cell/><cell>10</cell><cell/></row><row><cell>30</cell><cell>40</cell><cell>60</cell></row></table><p type="main"> <s>AND this mean Number forty will be di&longs;<lb/>
tant from the greate&longs;t Number ju&longs;t double the <lb/>
Interval which the Number of the Mean is <lb/>
di&longs;tant from the lea&longs;t Number; and the Con<lb/>
dition was, that the greate&longs;t Number &longs;hould <lb/>
bear that Portion to the lea&longs;t. </s> <s>By the Help of <lb/>
the&longs;e Mediocrites the Architects have di&longs;cover<lb/>
ed many excellent Things, as well with Rela<lb/>
tion to the whole Structure, as to its &longs;everal <lb/>
Parts; which we have not Time here to par<lb/>
ticularize. </s> <s>But the mo&longs;t common U&longs;e they <lb/>
have made of the&longs;e Mediocrities, has been how<lb/>
ever for their Elevations.</s></p>

<p type="head"> <s>CHAP. VII.</s></p>

<p type="head"> <s><emph type="italics"/>Of the Invention of Columns, their Dimen&longs;ions and Collocation.<emph.end type="italics"/></s></p>

<p type="main"> <s>It will not be unplea&longs;ant to con&longs;ider &longs;ome <lb/>
further Particulars relating to the three <lb/>
Sorts of Columns which the Ancients invent<lb/>
ed, in three different Points of Time: And it <lb/>
is not at all improbable, that they borrowed the <lb/>
Proportions of their Columns from that of the <lb/>
Members of the human Body. </s> <s>Thus they <lb/>
found that from one Side of a Man to the <lb/>
other was a &longs;ixth Part of his Height, and that <lb/>
from the Navel to the Reins was a tenth. </s> <s>From <lb/>
this Ob&longs;ervation the Interpreters of our &longs;acred <lb/>
Books, are of Opinion, that <emph type="italics"/>Noah<emph.end type="italics"/>'s Ark for <lb/>
the Flood was built according to the Propor<lb/>
tions of the human Body. </s> <s>By the &longs;ame Pro<lb/>
portions we may rea&longs;onably conjecture, that the <lb/>
Ancients erected their Columns, making the <lb/>
Height in &longs;ome &longs;ix Times, and in others ten <lb/>
Times, the Diameter of the Bottom of the