Common Geometry
Original
This, teacheth to measure, either at hand: and the practiser, to be by the thing Measured: and so, by due applying of Cumpase, Rule, Squire, Yarde, Ell, Perch, Pole, Line, Gaging rod, (or such like instrument) to the Length, Plaine, or Solide measured,
(1.)
* to be certified, either of the length, perimetry, or distance lineall: and this is called, Mecometrie. Or
(2.)
* to be certified of the content of any plaine Superficies: whether it be in ground Surueyed, Borde, or Glasse measured, or such like thing: which measuring, is named Embadometrie.
(3.)
* Or els to vnderstand the Soliditie, and content of any bodily thing: as of Tymber and Stone, or the content of Pits, Pondes, Wells, Vessels, small & great, of all fashions. Where, of Wine, Oyle, Beere, or Ale vessells, &c, the Measuring, commonly, hath a peculier name: and is called Gaging. And the generall name of these Solide measures, is Stereometrie.
(2.)
Or els, this vulgar Geometrie, hath consideration to teach the practiser, how to measure things, with good distance betwene him and the thing measured: and to vnderstand thereby, either
(1.)
* how Farre, a thing seene (on land or water) is from the measurer: and this may be called Apomecometrie:
(2.)
Or, how High or depe, aboue or vnder the leuel of the measurers stãding, any thing is, which is sene on land or water, called Hypsometrie.
(3.)
* Or, it informeth the measurer, how Broad any thing is, which is in the measurers vew: so it be on Land or Water, situated: and may be called Platometrie. Though I vse here to condition, the thing measured, to be on Land, or Water Situated:
yet, know for certaine, that the sundry heigthe of Cloudes, blasing Starres, and of the Mone, may (by these meanes) haue their distances from the earth: and, of the blasing Starres and Mone, the Soliditie (aswell as distances) to be measured: But because, neither these things are vulgarly taught: nor of a common practiser so ready to be executed: I, rather, let such measures be reckened incident to some of our other Artes, dealing with thinges on high, more purposely, then this vulgar Land measuring Geometrie doth: as in Perspectiue and Astronomie, &c.
Of these Feates (farther applied) is Sprong the Feate of Geodesie, or Land Measuring: more cunningly to measure & Suruey Land, Woods, and Waters, a farre of. More cunningly, I say: But God knoweth (hitherto) in these Realmes of England and Ireland (whether through ignorance or fraude, I can not tell, in euery particular)
how great wrong and iniurie hath (in my time) bene committed by vntrue measuring and surueying of Land or Woods, any way. And, this I am sure: that the Value of the difference, betwene the truth and such Surueyes, would haue bene hable to haue foũd (for euer) in eche of our two Vniuersities, an excellent Mathematicall Reader: to eche, allowing (yearly) a hundred Markes of lawfull money of this realme: which, in dede, would seme requisit, here, to be had (though by other wayes prouided for) as well, as, the famous Vniuersitie of Paris, hath two Mathematicall Readers: and eche, two hundreth French Crownes yearly, of the French Kinges magnificent liberalitie onely. Now, againe, to our purpose returning: Moreouer, of the former knowledge Geometricall, are growen the Skills of Geographie, Chorographie, Hydrographie, and Stratarithmetrie.
Musean translation
Modern machine-assisted Musean edition by Mouseia, from Dee's 1570 Praeface. Latin quotations and titles are translated into English, using Dee's own English glosses where provided. Printer's type-size markup is normalized; marginal notes are kept as asides. Billingsley's separate address is omitted. Uncertain readings are marked.
This teaches measuring either at hand, with the practitioner standing by the thing measured: and so, by duly applying the compass, rule, square, yard, ell, perch, pole, line, gaging rod (or the like instrument) to the length, plane, or solid being measured,
(1.)
To be certified of the length, perimeter, or linear distance: and this is called Mecometry. Or
(2.)
To be certified of the content of any plane surface: whether it be surveyed ground, a measured board or pane of glass, or the like thing: which measuring is named Embadometry.
(3.)
Or else to understand the solidity and capacity of any bodily thing: such as timber and stone, or the capacity of pits, ponds, wells, vessels small and great of all kinds. Where the measuring of wine, oil, beer, or ale vessels, etc., commonly has a peculiar name: and is called gaging. And the general name of these solid measures is stereometry.
(2.)
Or else this common geometry also undertakes to teach the practitioner how to measure things while standing at a good distance from the thing measured: and by that to understand either
(1.)
How far a thing seen (on land or water) is from the measurer: and this may be called Apomecometry:
(2.)
Or, how high or deep, above or below the level of the measurer's standing, anything is that is seen on land or water, called Hypsometry.
(3.)
Or, it informs the measurer how broad anything is that lies in the measurer's view, provided it is situated on land or water: and may be called Platometry. Though I am in the habit of stipulating that the thing measured be situated on land or water:
Yet know for certain that the various heights of clouds, comets, and the moon may by these means have their distances from the earth; and that of comets and the moon, the solidity as well as the distances may be measured. But because neither these things are taught in the common way, nor are so ready for the ordinary practitioner to carry out, I prefer to let such measures be reckoned as incidental to some of our other arts, which deal more purposely with things on high than this common land-measuring geometry does: as in perspective and astronomy, etc.
From these feats, further applied, has sprung the feat of geodesy, or land surveying: to measure and survey land, woods, and waters more skillfully from afar. More skillfully, I say: but God knows, up to now in these realms of England and Ireland (whether through ignorance or fraud, I cannot tell in every particular)
How great a wrong and injury has been done in my time by untrue measuring and surveying of land or woods in every way. And of this I am sure: that the value of the difference between the truth and such surveys would have been able to fund forever, in each of our two universities, an excellent mathematics reader: each allowed yearly a hundred marks of lawful money of this realm; which indeed would seem to be required here (though provided for in other ways), just as the famous University of Paris has two mathematics readers, each with two hundred French crowns yearly, from the French king's magnificent liberality alone.
Now, returning again to our purpose: moreover, from that earlier geometrical knowledge have grown the skills of geography, chorography, hydrography, and Stratarithmetrie.
Plain English translation
Modern machine-assisted Plain English edition by Mouseia, from Dee's 1570 Praeface. Latin quotations and titles are translated into English, using Dee's own English glosses where provided. Printer's type-size markup is normalized; marginal notes are kept as asides. Billingsley's separate address is omitted. Uncertain readings are marked.
This teaches measuring up close: the practitioner is at the thing being measured, and so, by correctly applying a compass, rule, square, yard, ell, perch, pole, line, gaging rod, (or such like instrument) to the length, plane, or solid being measured,
(1.)
* to learn either the length, perimeter, or linear distance; and this is called mecometry. Or
(2.)
* to learn the content of any plane surface: whether it is ground surveyed, board measured, or glass measured, or such like thing; which measuring is named embadometry.
(3.)
* Or else to understand the solidity and content of any bodily thing: as of timber and stone, or the content of pits, ponds, wells, vessels, small and great, of all shapes. Where the measuring of wine, oil, beer, or ale vessels, etc. commonly has a particular name, and is called gaging. And the general name of these solid measures is stereometry.
(2.)
Or else, this common geometry also aims to teach the practitioner how to measure things from a good distance, keeping apart from the thing measured, and by that to understand either
(1.)
* how far away a thing seen (on land or water) is from the measurer; and this may be called apomecometry:
(2.)
Or, how high or deep, above or below the level of the measurer's standing, anything seen on land or water is; called hypsometry.
(3.)
* Or, it tells the measurer how broad anything is that lies in the measurer's view, as long as it is situated on land or water; and may be called platometry. Though I make it a condition here that the thing measured be situated on land or water:
yet know for certain that the various heights of clouds, blazing stars, and the moon can (by these means) have their distances from the earth determined; and that the solidity of the blazing stars and the moon can be measured as well as their distances. But because these things are not commonly taught, nor so easily carried out by an ordinary practitioner, I prefer to count such measures as belonging to some of our other arts, which deal more purposely with things up high, rather than to this common land-measuring geometry: as in perspective and astronomy, etc.
From these feats (applied further) has sprung the feat of geodesy, or land measuring: to measure and survey land, woods, and waters more skillfully from afar. More skillfully, I say. But God knows (so far, in these realms of England and Ireland, whether through ignorance or fraud, I cannot tell in every particular)
how much wrong and injury has been done (in my time) by untrue measuring and surveying of land or woods, in any way. And this I am sure of: the value of the difference between the truth and such surveys could have kept (forever) an excellent mathematics reader in each of our two universities; allowing each (yearly) a hundred marks of lawful money of this realm, which indeed would seem to be needed here (though provided for in other ways), just as the famous University of Paris has two mathematics readers, each with two hundred French crowns a year, from the French king's magnificent generosity alone. Now, returning again to our purpose: moreover, from the earlier geometric knowledge have grown the skills of geography, chorography, hydrography, and Stratarithmetrie.
About this section
Common Geometry is part of The Mathematicall Praeface to the Elements of Geometrie by John Dee. This page sets the 16th-century English original beside 2 direct-source translations, so any line can be checked against the source. It is part 7 of 34 in the work, which is kept in the European tradition.
Open the work page for the full contents, every edition, and the download links, or go back to Explore to browse other complete works in the European tradition. The reader keeps your place when you are signed in and lets you compare the original with each translation, one edition at a time.