The Trail of '98: A Northland Romance

			Simple, Which dealeth with Numbers onely: and demonstrateth all their properties and appertenances: where, an Vnit, is Indiuisible.					In thinges Supernaturall, Æternall, & Diuine: By Application, Ascending.
		Arithmetike.	Mixt, Which with aide of Geometrie principall, demonstrateth some Arithmeticall Conclusion, or Purpose.				The vse whereof, is either,		The like Vses and Applications are, (though in a degree lower) in the Artes Mathematicall Deriuatiue.
	Principall, which are two, onely,							In thinges Mathematicall: without farther Application.
Sciences, and Artes Mathematicall, are, either			Simple, Which dealeth with Magnitudes, onely: and demonstrateth all their properties, passions, and appertenances: whose Point, is Indiuisible.
		Geometrie.						In thinges Naturall: both SubstÃtiall, & Accidentall, Visible, & Inuisible. &c. By Application: Descending.
			Mixt, Which with aide of Arithmetike principall, demonstrateth some Geometricall purpose, as EVCLIDES ELEMENTES.
			Arithmetike, vulgar: which considereth	Arithmetike of most vsuall whole numbers: And of Fractions to them appertaining. Arithmetike of Proportions. Arithmetike Circular. Arithmetike of Radicall Nũbers: Simple, Compound, Mixt: And of their Fractions. Arithmetike of Cossike Nũbers: with their Fractions: And the great Arte of Algiebar.
		The names of the Principalls: as,		At hand		All Lengthes.— All Plaines: As, Land, Borde, Glasse, &c. All Solids: As, Timber, Stone, Vessels, &c.		Mecometrie. Embadometrie. Stereometrie.
	Deriuatiue frÕ the Principalls: of which, some haue		Geometrie, vulgar: which teacheth Measuring			How farre, from the Measurer, any thing is: of him sene, on Land or Water: called Apomecometrie.		Geodesie: more cunningly to Measure and Suruey Landes, Woods, Waters. &c.
				With distÃce from the thing Measured, as,		How high or deepe, from the leuell of the Measurers standing, any thing is: Seene of hym, on Land or Water: called Hypsometrie.	Of which are growen the Feates & Artes of	Geographie. Chorographie. Hydrographie.
						How broad, a thing is, which is in the Measurers view: so it be situated on Land or Water: called Platometrie.		Stratarithmetrie.
			Perspectiue,		Which demonstrateth the maners and properties of all Radiations: Directe, Broken, and Reflected.
			Astronomie,		Which demonstrateth the Distances, Magnitudes, 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.
			Musike,		Which demonstrateth by reason, and teacheth by sense, perfectly to iudge and order the diuersitie of Soundes, hie or low.
			Cosmographie,		Which, wholy and perfectly maketh description of the Heauenlym and also Elementall part of the World: and of these partes, maketh homologall application, and mutuall collation necessary.
			Astrologie,		Which reasonably demonstrateth the operations 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.
			Statike,		Which demonstrateth the causes of heauines and lightnes of all thinges: and of the motions and properties to heauines and lightnes belonging.
			Anthropographie,		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, Characterization, & due Locall motion of any percell of the said body assigned: and of numbers to the said percell appertaining.
		Propre names as,	Trochilike,		Which demonstrateth the properties of all Circular motions: Simple and Compound.
			Helicosophie,		Which demonstrateth the designing of all Spirall lines: in Plaine, on Cylinder, Cone, SphÆre, ConoÏd, and SphÆroid: and their properties.
			Pneumatithmie,		Which demonstrateth by close hollow Geometricall figures (Regular and Irregular) the straunge properties (in motion or stay) of the Water, Ayre, Smoke, and Fire, in their Continuitie, and as they are ioyned to the Elementes next them.
			Menadrie,		Which demonstrateth, how, aboue Natures Vertue, and power simple: Vertue and force, may be multiplied: and so to directe, to lift, to pull to, and to put or cast fro, any multiplied, or simple determined Vertue, Waight, or Force: naturally, not, so, directible, or moueable.
			Hypogeiodie,		Which demonstrateth, how, vnder the SphÆricall Superficies of the Earth, at any depth, to any perpendicular line assigned (whose distance from the perpendicular of the entrance: and the Azimuth likewise, in respecte of the sayd entrance, is knowen) certaine way, may be prescribed and gone, &c.
			Hydragogie,		Which demonstrateth 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.
			Horometrie,		Which demonstrateth, how, at all times appointed, the precise, vsuall denomination of time, may be knowen, for any place assigned.
			Zographie,		Which demonstrateth and teacheth, how, the Intersection of all visuall Pyramids, made by any plaine assigned (the Center, distance, and lightes being determined) may be, by lines, and proper colours represented.
			Architecture,		Which is a Science garnished with many doctrines, and diuers Instructions: by whose iudgement, all workes by other workmen finished, are iudged.
			Nauigation,		Which demonstrateth, how, by the Shortest good way, by the aptest direction, and in the shortest time: a sufficient Shippe, betwene any two places (in passage nauigable) assigned, may be conducted: and in all stormes and naturall disturbances chauncing, how to vse the best possible meanes, to recouer the place first assigned.
			Thaumaturgike,		Which geueth certaine order to make straunge workes, of the sense to be perceiued: and of men greatly to be wondred at.
			Archemastrie,		Which teacheth to bring to actuall experience sensible, all worthy conclusions, by all the Artes Mathematicall purposed: and by true Naturall philosophie, 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 performance of complete Experiences: which, of no particular Arte, are hable (Formally) to be challenged.

THE ELEMENTS
OF GEOMETRIE
of the most auncient
Philosopher
EVCLIDE
of Megara.

Faithfully (now first) translated
into the Englishe toung, by
H. Billingsley, Citizen of London.
Whereunto are annexed certaine
Scholies, Annotations, and Inuentions,
of the best Mathematiciens,
both of time past, and
in this our age.

With a very fruitfull PrÆface made by M. I. Dee,
specifying the chiefe Mathematicall Sciẽces, what
they are, and wherunto commodious: where, also, are disclosed certaine new Secrets Mathematicall and Mechanicall, vntill these our daies, greatly missed.

Imprinted at London by Iohn Daye.

Transcriber’s Footnotes

A. Mathematical Notation. John Dee used the “root” sign √ in combination with some less familiar symbols:

‘power of 1’ symbol	“First power”, here used to express an unknown. Shown in this e-text as X (capitalized).
square root	Root sign combined with “second power” symbol = square root. Shown in this e-text as ²√.
cube root	Root sign combined with “third power” symbol = cube root. Shown in this e-text as ³√.
cube root	Doubled “second power” symbol = 4th power; with root sign = fourth root. Shown in this e-text as ⁴√.

B. Diagrams: The symbol drawn as P (Pounds) is shown here as P. See above for X symbol.

                            HOTE
                              +C
                              "
                              "
                              +
                              "
                              "
                              +
                              "
                              "
                              +E
                              "
MOIST                  A TEMPERATE                B     DRYE
+------+------+------+------+------+------+------+------+
                              "D
                              "
                              +
                              "
                              "
                              +
                              "
                              "
                              +
                              "
                              "
                              +
                            COLD

_____________________
" " "
" {P}. 2. " Hote. 4. "
" " "
" {P}. 1. " Hote. 3. "
"_________"___________"

_____________________
"         "           " _
" {P}. 2. " Hote. 4. "   ⅓ _   The forme_
"         "           "     _   3⅔ resulting.
" {P}. 1. " Hote. 3. " _ ⅔
"_________"___________"

C. “Vergilius teaches in his Georgikes.” The quoted lines, with breaks at each “&c.”, are 438-439; 451-457; 463-464.

Euclid citations

The following Propositions were identified by number.

6.12: (How) to find a fourth (line) proportional to three given straight lines.

11.34: In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciprocally proportional to the heights are equal.

11.36: If three straight lines are proportional, then the parallelepipedal solid formed out of the three equals the parallelepipedal solid on the mean which is equilateral, but equiangular with the aforesaid solid.

12.1: Similar polygons inscribed in circles are to one another as the squares on their diameters.

12.2: Circles are to one another as the squares on their diameters.

12.18 (“last”): Spheres are to one another in triplicate ratio of their respective diameters.

Notes on the text

The Greek letter η (eta) was consistently printed as if it were the ou-ligature ȣ.

The Latin -que was written as an abbreviation resembling -q´;. It is shown here as q^ue.

Less common words include “fatch” (probably used as a variant of “fetch”) and the mathematical terms “sexagene” and “sexagesme”.

Title: The Trail of '98

A Northland Romance

Author: Robert W. Service

Language: English

Character set encoding: ISO-8859-1

We were in a caldron of fire. The roar of doom was in our ears (page 143)
We were in a caldron of fire. The roar of doom was in our ears (page 143)

THE TRAIL OF ’98

A Northland Romance

ROBERT W. SERVICE

Author of

"The Spell of the Yukon" and "Ballads of a Cheechako"

With illustrations by

MAYNARD DIXON

emblem

NEW YORK

DODD, MEAD AND COMPANY

1911

DODD, MEAD AND COMPANY

Entered at Stationers' Hall

THE QUINN & BODEN CO. PRESS

RAHWAY, N. J.

Clyx.com

Title Page Text

THE ELEMENTS OF GEOMETRIE of the most auncient Philosopher EVCLIDE of Megara.

Faithfully (now first) translated into the Englishe toung, by H. Billingsley, Citizen of London. Whereunto are annexed certaine Scholies, Annotations, and Inuentions, of the best Mathematiciens, both of time past, and in this our age.