Part 3024

<hw>De*ter"mi*nant</hw>, <tt>n.</tt>

<p><b>1.</b> <def>That which serves to determine; that which causes determination.</def>

<p><b>2.</b> <fld>(Math.)</fld> <def>The sum of a series of products of several numbers, these products being formed according to certain specified laws; thus, the <i>determinant</i> of the nine numbers.</def>

<matrix><row>a, b, c,</row><row>a\'b7, b\'b7, c\'b7,</row><row>a\'b7\'b7, b\'b7\'b7, c\'b7\'b7,</row></matrix>

is <mathex>a b\'b7 c\'b7\'b7 -- a b\'b7\'b7 c\'b7 + a\'b7 b\'b7\'b7 c] -- a\'b7 b c\'b7\'b7 + a\'b7\'b7 b\'b7 c</mathex>. The determinant is written by placing the numbers from which it is formed in a square between two vertical lines. The theory of <i>determinants</i> forms a very important branch of modern mathematics.

<p><b>3.</b> <fld>(Logic)</fld> <def>A mark or attribute, attached to the subject or predicate, narrowing the extent of both, but rendering them more definite and precise.</def>

<i>Abp. Thomson.</i>

<h1>Determinate</h1> <Xpage=401>

<hw>De*ter"mi*nate</hw> <tt>(?)</tt>, <tt>a.</tt> <ety>[L. <ets>determinatus</ets>, p. p. of <ets>determinare</ets>. See <er>Determine</er>.]</ety>

<p><b>1.</b> <def>Having defined limits; not uncertain or arbitrary; fixed; established; definite.</def>

<blockquote>Quantity of words and a <b>determinate</b> number of feet. <i>Dryden.</i></blockquote>

<p><b>2.</b> <def>Conclusive; decisive; positive.</def>

<blockquote>The <b>determinate</b> counsel and foreknowledge of God. <i>Acts ii. 23.</i></blockquote>

<p><b>3.</b> <def>Determined or resolved upon.</def> <mark>[Obs.]</mark>

<blockquote>My <b>determinate</b> voyage. <i>Shak.</i></blockquote>

<p><b>4.</b> <def>Of determined purpose; resolute.</def> <mark>[Obs.]</mark>

<blockquote>More <b>determinate</b> to do than skillful how to do. <i>Sir P. Sidney.</i></blockquote>

<cs><col>Determinate inflorescence</col> <fld>(Bot.)</fld>, <cd>that in which the flowering commences with the terminal bud of a stem, which puts a limit to its growth; -- also called <i>centrifugal inflorescence<i>.</cd> -- <col>Determinate problem</col> <fld>(Math.)</fld>, <cd>a problem which admits of a limited number of solutions.</cd> -- <mcol><col>Determinate quantities</col>, <col>Determinate equations</col></mcol> <fld>(Math.)</fld>, <cd>those that are finite in the number of values or solutions, that is, in which the conditions of the problem or equation determine the number.</cd></cs>

<h1>Determinate</h1> <Xpage=401>

<hw>De*ter"mi*nate</hw> <tt>(?)</tt>, <tt>v. t.</tt> <def>To bring to an end; to determine. See <er>Determine</er>.</def> <mark>[Obs.]</mark>

<blockquote>The sly, slow hours shall not <b>determinate</b> The dateless limit of thy dear exile. <i>Shak.</i></blockquote>

<h1>Determinately</h1> <Xpage=401>

<hw>De*ter"mi*nate*ly</hw> <tt>(?)</tt>, <tt>adv.</tt>

<p><b>1.</b> <def>In a determinate manner; definitely; ascertainably.</def>

<blockquote>The principles of religion are already either <b>determinately</b> true or false, before you think of them. <i>Tillotson.</i></blockquote>

<p><b>2.</b> <def>Resolutely; unchangeably.</def>

<blockquote>Being <b>determinately</b> . . . bent to marry. <i>Sir P. Sidney.</i></blockquote>

<h1>Determinateness</h1> <Xpage=401>