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authorRoger Frank <rfrank@pglaf.org>2025-10-15 01:46:58 -0700
committerRoger Frank <rfrank@pglaf.org>2025-10-15 01:46:58 -0700
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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+<title>The Groundplat</title>
+<meta http-equiv = "Content-Type" content = "text/html; charset=UTF-8">
+
+
+<style type = "text/css">
+
+body {margin-left: 10%; margin-right: 10%;}
+
+hr {width: 80%; margin-top: 1em; margin-bottom: 1em;}
+
+p {margin-top: .25em; margin-bottom: .25em; line-height: normal;}
+p.center {text-align: center;}
+
+
+/* tables */
+
+table {margin-left: auto; margin-right: auto; margin-top: 1em; margin-bottom: 1em;}
+
+table.groundplat {font-size: 87%; border-collapse: collapse;}
+
+td {vertical-align: middle; text-align: left; padding: .2em;
+/*border: 1px dotted #999;*/}
+
+td.number {text-align: right;}
+td.lower {vertical-align: bottom;}
+td.upper {vertical-align: top;}
+
+td.bracket {padding: .25em .1em;}
+
+td.bracket.leftline {padding-left: 1em; background-repeat: repeat-y; background-position: center left; background-image: url("../images/leftline.gif");}
+td.bracket.rightline {padding-right: 1em; background-repeat: repeat-y; background-position: center right; background-image: url("../images/rightline.gif");}
+
+td.bracket.lefttop {padding-left: 1em; background-repeat: no-repeat; background-position: bottom left; background-image: url("../images/topleft.gif");}
+td.bracket.righttop {padding-right: 1em; background-repeat: no-repeat; background-position: bottom right; background-image: url("../images/topright.gif");}
+
+td.bracket.leftbottom {padding-left: 1em; background-repeat: no-repeat; background-position: top left; background-image: url("../images/bottomleft.gif");}
+td.bracket.rightbottom {padding-right: 1em; background-repeat: no-repeat; background-position: top right; background-image: url("../images/bottomright.gif");}
+
+td.bracket.single {padding-right: 1em; background-repeat: no-repeat; background-position: center right;
+background-image: url("../images/bracket3_rt.gif");}
+
+
+/* conditional */
+table p {margin-top: 0em; line-height: normal;}
+
+/* sizes */
+.larger {font-size: 120%;}
+.largest {font-size: 150%;}
+
+
+/* my additions */
+
+p.mynote {background-color: #DDE; color: #000; padding: 1em;
+margin: 1em 5%; font-family: sans-serif; font-size: 90%;}
+
+</style>
+</head>
+
+<body>
+
+<p class = "mynote">
+Return to <a href = "../main.html#groundplat">John Dee’s Preface</a>.
+</p>
+
+<p class = "center"><i>J. DEE</i></p>
+
+<p class = "center largest">Here haue you (according to my promisse) the Groundplat of</p>
+
+<p class = "center larger">my MATHEMATICALL Præface: annexed to <i>Euclide</i> (now first)</p>
+
+<p class = "center">published in our Englishe tounge. An. 1570. Febr. 3.</p>
+
+
+<table class = "groundplat">
+
+<!-- principal, 6 rows -->
+<!-- row 1 of 6 -->
+
+<tr>
+<td class = "bracket righttop" rowspan = "3">
+&nbsp;
+</td>
+<td class = "bracket righttop" rowspan = "2">
+&nbsp;
+</td>
+<td class = "bracket righttop">
+&nbsp;
+</td>
+<td class = "lower" colspan = "4">
+<p><i><span class = "larger">Simple,</span> <span class = "small">Which dealeth with Numbers onely: and demon&shy;strateth all their properties and apper&shy;tenances: where, an Vnit, is Indiui&shy;sible.</span></i></p>
+</td>
+<td class = "bracket lefttop">
+&nbsp;
+</td>
+<td class = "bracket righttop">
+&nbsp;
+</td>
+<td rowspan = "2">
+<p class = "small"><i>In thinges Super&shy;naturall, æternall, &amp; Diuine: By Appli&shy;cation</i>, Ascending.</p></td>
+<td class = "bracket lefttop">
+&nbsp;
+</td>
+</tr>
+
+<!-- row 2 of 6 -->
+<tr>
+<!-- <td></td> <td></td> -->
+<td class = "bracket rightline">
+<p class = "larger">Arithmetike.</p>
+</td>
+<td colspan = "4" rowspan = "2">
+<p><i><span class = "larger">Mixt</span>, <span class = "small">Which with aide of Geometrie principall, demon&shy;strateth some Arith&shy;meticall Conclusion, or Purpose.</span></i></p>
+</td>
+<td class = "bracket leftline" rowspan = "4">
+&nbsp;
+</td>
+<td class = "bracket rightline" rowspan = "4">
+<p><i><span class = "larger">The vse</span><br>
+whereof, is either,</i></p>
+</td>
+<!-- <td></td> -->
+<td class = "bracket leftline" rowspan = "4">
+<p><i><span class = "small">The like Vses and Appli&shy;cations are, (though in a degree lower) in the</span></i> Artes Mathe&shy;maticall Deriuatiue.</p>
+</td>
+</tr>
+
+<!-- row 3 of 6 -->
+<tr>
+<!-- <td></td> -->
+<td class = "bracket rightline" rowspan = "2">
+<p><i><span class = "larger">Principall,</span> which are two, onely,</i></p>
+</td>
+<td class = "bracket rightbottom">
+<p>&nbsp;<br>&nbsp;</p>
+</td>
+<!-- <td></td> <td></td> <td></td> <td></td> <td></td> -->
+<td rowspan = "2">
+<p class = "small"><i>In thinges Mathe&shy;maticall: without farther Appli&shy;cation.</i></p>
+</td>
+<!-- <td></td> -->
+</tr>
+
+<!-- row 4 of 6 -->
+<tr>
+<td class = "bracket rightline" rowspan = "6">
+<p><span class = "largest">Sciences, and Artes Mathe&shy;maticall,</span> <span class = "larger">are, either</span></p>
+</td>
+<!-- <td></td> -->
+<td class = "bracket righttop">
+<p>&nbsp;<br>&nbsp;</p>
+</td>
+<td colspan = "4" rowspan = "2">
+<p><i><span class = "larger">Simple</span>, <span class = "small">Which dealeth with Magni&shy;tudes, onely: and demon&shy;strateth all their properties, passions, and apper&shy;tenances: whose Point, is Indiui&shy;sible.</span></i></p>
+</td>
+<!-- <td></td> <td></td> <td></td> <td></td> -->
+</tr>
+
+<!-- row 5 of 6 -->
+<tr>
+<!-- <td></td> -->
+<td class = "bracket rightbottom">
+<p>&nbsp;<br>&nbsp;</p>
+</td>
+<td class = "bracket rightline">
+<p class = "larger">Geometrie.</p>
+</td>
+<!-- <td></td> <td></td> <td></td> <td></td> <td></td> -->
+<td rowspan = "2">
+<p class = "small"><i>In thinges Naturall: both Substã&shy;tiall, &amp; Accidentall, Visible, &amp; Inuisible. &amp;c. By Appli&shy;cation:</i> Descending.</p>
+</td>
+<!-- <td></td> -->
+</tr>
+
+<!-- row 6 of 6 -->
+<tr>
+<!-- <td></td> -->
+<td>
+&nbsp;
+</td>
+<td class = "bracket rightbottom">
+&nbsp;
+</td>
+<td class = "upper" colspan = "4">
+<p><i><span class = "larger">Mixt</span>, <span class = "small">Which with aide of Arith&shy;metike principall, demon&shy;strateth some Geometricall purpose, as</span></i> EVCLIDES ELEMENTES.</p>
+</td>
+<td class = "bracket leftbottom">
+&nbsp;
+</td>
+<td class = "bracket rightbottom">
+&nbsp;
+</td>
+<!-- <td></td> -->
+<td class = "bracket leftbottom">
+&nbsp;
+</td>
+</tr>
+
+<!-- derivative, 5 rows -->
+<!-- row 1 of 5 -->
+
+<tr>
+<!-- <td></td> -->
+<td class = "bracket righttop" rowspan = "2">
+&nbsp;
+</td>
+<td class = "bracket righttop">
+&nbsp;
+</td>
+<td class = "lower bracket single">
+<p><span class = "larger">Arith&shy;metike,</span> <span class = "small"><i>vulgar: which consi&shy;dereth</i></span></p>
+</td>
+<td colspan = "7">
+<p>Arith&shy;metike of most vsuall whole numbers: And of Fractions to them apper&shy;taining.</p>
+<p>Arith&shy;metike of Propor&shy;tions.</p>
+<p>Arith&shy;metike Circular.</p>
+<p>Arith&shy;metike of Radicall Nũbers: Simple, Compound, Mixt: And of their Fractions.</p>
+<p>Arith&shy;metike of Cossike Nũbers: with their Fractions: And the great Arte of Algiebar.</p>
+</td>
+</tr>
+
+<!-- row 2 of 5 -->
+<tr>
+<!-- <td></td> <td></td> -->
+<td class = "lower bracket rightline">
+<p><i><span class = "larger">The names of</span> the Princi&shy;palls: as,</i></p>
+</td>
+<td class = "bracket righttop">
+&nbsp;
+</td>
+<td class = "bracket single" colspan = "2">
+<p class = "larger"><i>At hand</i></p>
+</td>
+<td class = "bracket single" colspan = "3">
+<p>All Lengthes.&mdash;</p>
+<p>All Plaines: As, Land, Borde, Glasse, &amp;c.</p>
+<p>All Solids: As, Timber, Stone, Vessels, &amp;c.</p>
+</td>
+<td colspan = "2">
+<p class = "larger">Mecometrie.</p>
+<p class = "larger">Embadometrie.</p>
+<p class = "larger">Stereometrie.</p>
+</td>
+</tr>
+
+<!-- row 3 of 5 -->
+<tr>
+<!-- <td></td> -->
+<td class = "bracket rightline" rowspan = "3">
+<p><i><span class = "larger">Deriuatiue</span> frõ the Princi&shy;palls: of which, some haue</i></p>
+</td>
+<td class = "bracket rightbottom">
+&nbsp;
+</td>
+<td class = "upper bracket rightline">
+<p><span class = "larger">Geometrie,</span> <span class = "small"><i>vulgar: which teacheth Measuring</i></span></p>
+</td>
+<td class = "bracket righttop" colspan = "2">
+&nbsp;
+</td>
+<td class = "lower">
+<p><i><span class = "larger">How farre</span>, <span class = "small">from the Measurer, any thing is: of him sene, on Land or Water: called</span></i> <span class = "larger">Apomecometrie</span>.</p>
+</td>
+<td class = "bracket lefttop">
+&nbsp;
+</td>
+<td class = "bracket righttop">
+&nbsp;
+</td>
+<td class = "lower" colspan = "2">
+<p><span class = "larger">Geodesie:</span> <span class = "small"><i>more cunningly to Measure and Suruey Landes, Woods, Waters. &amp;c.</i></span></p>
+</td>
+</tr>
+
+<!-- row 4 of 5 -->
+<tr>
+<td class = "bracket rightbottom" rowspan = "2">
+&nbsp;
+</td>
+<!-- <td></td> -->
+<td rowspan = "2">
+&nbsp;
+</td>
+<td class = "bracket rightbottom">
+&nbsp;
+</td>
+<td class = "upper bracket rightline" colspan = "2">
+<p><i><span class = "larger">With distãce</span> <span class = "small">from the thing Measured, as,</span></i></p>
+</td>
+<td>
+<p><i><span class = "larger">How high or deepe</span>, <span class = "small">from the leuell of the Measurers standing, any thing is: Seene of hym, on Land or Water: called</span></i> <span class = "larger">Hypso&shy;metrie</span>.</p>
+</td>
+<td class = "bracket leftline">
+&nbsp;
+</td>
+<td class = "bracket rightline">
+<p><i><span class = "larger">Of which</span> are growen the Feates &amp; Artes of</i></p>
+</td>
+<td colspan = "2">
+<p><span class = "larger">Geographie.</span></p>
+<p>&nbsp;</p>
+<p><span class = "larger">Choro&shy;graphie.</span></p>
+<p>&nbsp;</p>
+<p><span class = "larger">Hydro&shy;graphie.</span></p>
+</td>
+</tr>
+
+<!-- row 5 of 5 -->
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td>
+&nbsp;
+</td>
+<td class = "bracket rightbottom" colspan = "2">
+&nbsp;
+</td>
+<td>
+<p><i><span class = "larger">How broad</span>, <span class = "small">a&nbsp;thing is, which is in the Measurers view: so it be situated on Land or Water: called</span></i> <span class = "larger">Plato&shy;metrie</span>.</p>
+</td>
+<td class = "bracket leftbottom">
+&nbsp;
+</td>
+<td class = "bracket rightbottom">
+&nbsp;
+</td>
+<td class = "upper" colspan = "2">
+<p><span class = "larger">Strat&shy;arith&shy;metrie.</span></p>
+</td>
+</tr>
+
+<!-- proper names, 19 rows -->
+
+<tr>
+<td rowspan = "19">&nbsp;</td>
+<td class = "bracket rightline" rowspan = "8">
+&nbsp;
+</td>
+<td class = "bracket righttop">
+<p>&nbsp;<br>&nbsp;</p>
+</td>
+<td class = "upper" colspan = "2">
+<p class = "larger">Perspectiue,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth the maners and properties of all Radia&shy;tions: Directe, Broken, and Reflected.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> -->
+<td class = "bracket rightline" rowspan = "6">
+&nbsp;
+</td>
+<td class = "upper" colspan = "2">
+<p class = "larger">Astro&shy;nomie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth the Distances, Magni&shy;tudes, and all Naturall motions, Apparences, and Passions, proper to the Planets and fixed Starres: for any time, past, present, and to come: in respecte of a certaine Horizon, or without respecte of any Horizon.</i></p>
+</td>
+</tr>
+
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Musike,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth by reason, and teacheth by sense, perfectly to iudge and order the diuer&shy;sitie of Soundes, hie or low.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Cosmo&shy;graphie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which, wholy and perfectly maketh description of the Heauenlym and also Elementall part of the World: and of these partes, maketh homologall appli&shy;cation, and mutuall collation necessary.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Astro&shy;logie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which reasonably demon&shy;strateth the opera&shy;tions and effectes of the naturall beames of light, and secrete Influence of the Planets, and fixed Starres, in euery Element and Elementall body: at all times, in any Horizon assigned.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Statike,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth the causes of heauines and lightnes of all thinges: and of the motions and properties to heauines and lightnes belonging.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Anthropographie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which describeth the Nũber, Measure, Waight, Figure, Situation, and colour of euery diuers thing contained in the perfecte body of MAN: and geueth certaine knowledge of the Figure, Symmetrie, Waight, Charac&shy;terization, &amp; due Locall motion of any percell of the said body assigned: and of numbers to the said percell apper&shy;taining.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> -->
+<td class = "bracket rightline" rowspan = "3">
+<p><i><span class = "larger">Propre names</span><br>
+as,</i></p>
+</td>
+<td class = "upper" colspan = "2">
+<p class = "larger">Trochilike,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth the properties of all Circular motions: Simple and Compound.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> -->
+<td class = "bracket rightbottom" rowspan = "2">
+&nbsp;
+</td>
+<!-- <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Helico&shy;sophie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth the designing of all Spirall lines: in Plaine, on Cylinder, Cone, Sphære, Conoïd, and Sphæroid: and their properties.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Pneuma&shy;tithmie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth by close hollow Geometricall figures (Regular and Irregular) the straunge properties (in motion or stay) of the Water, Ayre, Smoke, and Fire, in their Conti&shy;nuitie, and as they are ioyned to the Elementes next them.</i></p>
+</td>
+</tr>
+
+<tr>
+<!-- <td></td> -->
+<td rowspan = "9">
+&nbsp;
+</td>
+<td class = "bracket rightline" rowspan = "8">
+&nbsp;
+</td>
+<td class = "upper" colspan = "2">
+<p class = "larger">Menadrie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth, how, aboue Natures Vertue, and power simple: Vertue and force, may be multi&shy;plied: and so to directe, to lift, to pull to, and to put or cast fro, any multi&shy;plied, or simple deter&shy;mined Vertue, Waight, or Force: naturally, not, so, direc&shy;tible, or moueable.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Hypogeiodie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth, how, vnder the Sphæricall Super&shy;ficies of the Earth, at any depth, to any perpen&shy;dicular line assigned (whose distance from the perpen&shy;dicular of the entrance: and the Azimuth likewise, in respecte of the sayd entrance, is knowen) certaine way, may be prescribed and gone, &amp;c.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Hydra&shy;gogie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth the possible leading of water by Natures law, and by artificiall helpe, from any head (being Spring, standing, or running water) to any other place assigned.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Horometrie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth, how, at all times appointed, the precise, vsuall denomi&shy;nation of time, may be knowen, for any place assigned.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Zographie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth and teacheth, how, the Inter&shy;section of all visuall Pyramids, made by any plaine assigned (the Center, distance, and lightes being deter&shy;mined) may be, by lines, and proper colours repre&shy;sented.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Archi&shy;tecture,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which is a Science garnished with many doctrines, and diuers Instructions: by whose iudgement, all workes by other workmen finished, are iudged.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Nauigation,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which demon&shy;strateth, how, by the Shortest good way, by the aptest direction, and in the shortest time: a&nbsp;suffi&shy;cient Shippe, betwene any two places (in passage nauigable) assigned, may be conducted: and in all stormes and naturall distur&shy;bances chauncing, how to vse the best possible meanes, to recouer the place first assigned.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> <td></td> -->
+<td class = "upper" colspan = "2">
+<p class = "larger">Thaumaturgike,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which geueth certaine order to make straunge workes, of the sense to be perceiued: and of men greatly to be wondred at.</i></p>
+</td>
+</tr>
+<tr>
+<!-- <td></td> <td></td> -->
+<td class = "bracket rightbottom">
+&nbsp;
+</td>
+<td class = "upper" colspan = "2">
+<p class = "larger">Arche&shy;mastrie,</p>
+</td>
+<td colspan = "6">
+<p class = "small"><i>Which teacheth to bring to actuall experience sensible, all worthy conclu&shy;sions, by all the Artes Mathe&shy;maticall purposed: and by true Naturall philo&shy;sophie, concluded: And both addeth to them a farder Scope, in the termes of the same Artes: and also, by his proper Method, and in peculiar termes, procedeth, with helpe of the forsayd Artes, to the perfor&shy;mance of complete Experi&shy;ences: which, of no parti&shy;cular Arte, are hable (Formally) to be challenged.</i></p>
+</td>
+</tr>
+</table>
+
+<p class = "mynote">
+Return to <a href = "../main.html#groundplat">John Dee’s Preface</a>.
+</p>
+
+</body>
+</html>