DEFINITIONS



A Cord,  or Subtense, is a right line, drawn from the one extre­
mity to the other of an Arch. 

2. A right Sine  is the half Cord of the double Arch proposed,
and from one extremity of the Arch falleth perpendicularly on the 
Radius, passing by the other end thereof.

3. A Tangent  is a right line, drawn from the Secant by one end of
the Arch, perpendicularly on the extremity of the Diameter, passing
by the other end of the said Arch.

4. A Secant  is the prolonged Radius, which passeth by the upper
extremity of the Arch, till it meet with the sine Tangent of the 
said Arch.

5. Complement  is the difference betwixt the lesser Arch, and a 
Quadrant, or betwixt a right Angle and an Acute.

6. The complement to a semi-Circle,  is the difference betwixt the
half-Circumference and any Arch lesser, or betwixt two right An­
gles, and an Oblique Angle, whither blunt or sharp.

7. The versed sine  is the remainder of the Radius, the sine



Complement being subtracted from it, and though great use may be
made of the versed sines, for finding out of the Angles by the sides,
and sides by the Angles: yet in Logarirhmicall calculations they 
are altogether useless, and therefore in my Trissotetras there is no
mention made of them.

8. In Amblygone sphericalls,  which admit both of an Extrinsecall,
and Intrinsecall demission of the perpendicular, ninteen severall
parts are to be considered: viz. The Perpendicular, the Subten­
dentall, the Subtendentine, two Cosubtendents, the Basall, the Basi­
dion, the chief Segment of the Base, two Cobases, the double Ver­
ticall, the Verticall, the Vertical line, two Coverticalls, the next Ca­
thetopposite, the prime Cathe opposite, and the two Cocathetoppo­
sites: fourteen whereof, (to wit) the Subtendentall, the Subtenden­
tine, the Cosubtendents, the Basall, the Basidion, the Cobases, the
Verticall, the Verticaline, the Coverticalle, and Cocathetopposites,
are called the first, either Subtendent, Base, Topangle, or Cocathe­
topposite, whither in the great Triangle or the little, or in the Cor­
rectangle, if they be ingredients of that Rectanglar, whereof most
parts are known, which parts are alwayes a Subtendent and a Ca­
thetopposite: but if they be in the other Triangle, they are called 
the second Subtendents, Bases, and so forth.

9. The externall double Verticall  is included by the Perpendicu­
lar, and Subtendentall, and divided by the Subtendentine,: the inter­
nall is included by cosubtendents, and divided by the Perpendicular.







A Lexicidion of some of the hardest
words, that occurre in the discourse of this
institution Trigonometricall.


BEing certainly perswaded, that a great many
good spirits ply Trigonometry, that are not ver­
sed in the learned Tongues, I thought fit, for
their encouragement, to subjoyne here the ex­
plication of the most important of those Greek, and Latin
termes, which, for the more efficacy of expression, I have
made use of in this Treatise: in doing whereof, that I
might both instruct the Reader, and not weary him, I have
endeavoured perspicuity with shortnesse: though (I speak it
ingenuously) to have been more prolixe therin, could have
cost but very little labor to me, who have already bin pret­
ty well versed in the like, as may appear by my Etymolo­
gicall dictionary of above twenty seven thousand proper
names, mentioned in the Lemmas of my serveall Volums of 
Epigrams, the words whereof are for the most part abstru­
ser, derived from moe Languages, and more liable to
large, and ample interpretations. However (cæteris paribus)
brevity is to be preferred; therefore let us proceed to the 
Vocabulary in hand.






THE LEXICIDION.


A.

ACute,  comes from Acuo, acuere, to sharpen, and is said
of an Angle, whose including sides, the more that its mea­
sure is lesse then a Quadrant, have their concursive, and
angulary point the more penetrative, sharp, keen and pierce­
ing: Whence an acutangled triangle.


Adæquat,  is that, which comprehendeth to the full, whatever is in the
thing to the which it is compared, and for the most part in my Tris­
soretras is said of the generall finall Resolvers, in relation to the 
Moods resolved by them. It is compounded of Ad, and æquo, æ­
quare, parem facere, to make one thing altogether like, or equall to
another.


Adjacent,  signifieth to lie neare, and close, and is applyed both to sides,
and Angles, in which sense likewise I make use of the words adjoyn­
ing the, conterminat, or conterminall with, annexed to, intercepted in,
and other such like, for the more variety, as adherent, bounding,
bordering, and so forth: It comes from Adjaceo, Adjacere, to lie
neere unto, as the words Ad and jaceo, which are the parts whereof
it is compounded, most perspicuously declare.


Additionall,  is said of the Line, which, in my comment, is indiffer­
rently called the Line of Addition, the Line of continuation, the ex­
trinsecall Line, the excesse of the Secant above the Radius, the Re­
siduum, or the new Secant: it comes from Addo, Addere, which is
compounded of Ad, and do, to put to and augment.


Affection,  is the nature, passion, and quality of an Angle, and consist­
eth either in the obtusity, acutenesse, or rectitude thereof: It is
a verball from Afficio, affeci, affectum, compounded of ad, and facio.




Aggregat,  is the summe, totall, or result of an Addition, and is com­
pounded of Ad, and grex; for, as the Shepheard gathers his Sheep
into a flock, so doth the Arithmetician compact his numbers to be
added into a summe.


Alternat,  is said of Angles, made by a Line cutting two or more pa­
rallels, which Angles may be properly called so; because they differ in
nothing else but their situation; for of the sectionary Line, to the which
I suppose the parallels to be fixed, have the highest and lowest points
thereof to interchange their sites, by a motion progressive towards the 
roome of the under Alternat, and terminating in that of the
upper one, we will find, that both the inclination of the Lines towards
one another, and the quality of the Angles, will, notwithstanding that
alteration, be the same as before; hence it is that they are called al­
ternat, because there is no other difference betwixt them: or, if al­
ternat be taken ( as arithmetically it is ) for that proportion, wherein
the Antecedent is compared to the Antecedent, and the Consequent to
the Consequent, the sense will likewise hold in the foresaid Angles; for if
by the parallelisme of two right Lines, cut with a third, two blunt, and 
two keen Angles be produced ( as must needs, unlesse the Secant line
be to the parallels a perpendicular) the keen or acute Angle will be
to its complement, or successively following obtuse Angle, as the o­
ther acute unto its following obtuse; therefore alternly, as the An­
tecedents are to one another, viz. the Acute to the Acute: so the Con­
sequents, the obtuse to the obtuse. And if the Angles be right, the di­
rect and alternat proportion is one and the same; the third, and
fourth terms of the Analogy being in nothing different from the first,
and second.


Ambient,  is taken for any of the legs of a rectangle, or the including,
containing, or comprehending sides of the right Angle: it comes from
Ambio, Ambite, which is compounded of Am and eo, i.e. circu­
meo, and more properly applied to both, then to any one of them, though
usually it be usurped for one alone, vide Leg.


Amblygonian,  is said of obtuse angled Triangles, and Amblygonosphe­
ricall of obtuse sphericals: It is composed of [GREEK], and [GREEK] an­
gulus.


Amfractuosities,  are taken here for the cranklings, windings, turnings,
and involutions belonging to the equisoleary Scheme; of am and fran­
go, quod sit quasi via crebris mæandris undequaque interrupta.




Analogy,  signifieth an equality of proportion, a likenesse of reasons, a 
conveniencie, or habitude betwixt termes: It is compounded of [GREEK] , æ­
qualiter, and [GREEK] , ratio.


Analytick,  resolutory, and is said of those things, that are resolved into
their first principles, of [GREEK] , re, and [GREEK] solvo.


Antilogarithm,  is the Logarithm of the complement: as for example,
the Anti-logarithm of a Sine is the Logarithm of the Sine complement,
vide Logarithm.


Anti-secant, Anti-sine, and Anti-tangent,  are the complements of the 
Secant, Sine and Tangent, and are called sometime Co-secant, Co-sine,
and Co-tangent: they have anti prefixed, because they are not in the
same colume, and co, because they are in the next to it.


Apodictick,  is that, which is demonstrative, and giveth evident proofs
of the truth of a conclusion; of [GREEK] and [GREEK], monstro, osten­
do, unde [GREEK], demonstratio.


Area,  is the capacity of a Figure, and whole content thereof.


Arch, or Ark,  is the segment of a circumference lesse then a semicircle: ma­
jor Arch is above 45. degrees, a minor Arch, lesse then 45. vide Circle.


Arithmeticall complement,  is the difference between the Logarithm to
be substracted, and that of the double, or single Radius.


Artificiall numbers,  are the Logarithms, and artificiall Sine the Loga­
rithm of the Sine.


Axiome,  is a maxim, tenet, or necessary principle, whereupon the Sci­
ence of a thing is grounded: it cometh from [GREEK], dignus; because
such things are worthy our knowledge.


B.

BAsall,  adjectively is that, which belongeth to the Base, or the sub­
jacent side, but substantively the great Base.


Basangulary,  is said of the Angles at the Base. 


Basidion, or baset,  is the little Base, all which come from the Greek word
[GREEK],[GREEK]


Basiradius,  is the totall Sine of that Arch, a Segment whereof is the Base
of the proposed sphericall Triangle.


Bisected, and Bisegment,  are said of lines cut into two equall parts; it 
comes from biseco, bisecare, bisectum, bisegmen.


Bluntnesse, or flatnesse,  is the obtuse affection of Angles.




Bucarnon,  by this name is entitled the seven and fortieth proposition of
the first of the elements of Euclid; because of the oxe, or, ( as some
say) the hecatomb which Pythagoras, for gladnesse of the invention,
sacrificed unto the gods: of [GREEK], bos, and [GREEK], vicissim aliquid
capio; they being ( as it is supposed ) well pleased with that acknow­
ledgement of his thankfulnesse for so great a favour, as that was,
which he received from them: you may see the proposition in the se­
venteenth of my Apodicticke.


C.

CAnon,  is taken here for the Table of Sines and Tangents, or of
their Logarithms: it properly signifieth the needle or tongue of a 
balance, and metaphorically a rule, whereby things are examined.


Cases,  are the parts wherein a Mood is divided from cado.


Cathetos,  is a Perpendicular line, from [GREEK], demitto, of [GREEK], and [GREEK]


Catheteuretick,  is concerning the finding out of the Perpendicular
of [GREEK], and [GREEK], [GREEK], invenio.


Cathetobasall,  is said of the Concordances of Loxogenoshericall Moods,
in the Datas of the Perpendicular, and the Base, for finding out of the
maine quæsitum.


Cathet opposite,  is the Angle opposite to the Perpendicular; it is a 
hybrid or mungrell word, composed of the Greek [GREEK], and Latin
oppositus.


Cathet orabdos, or Cathetoradius,  is the totall Sine of that Arch, a
Segment whereof is the Cathetos, or Perpendicular of the proposed
Orthogonosphericall.


Cathetothesis, and cathetothetick  are said of the determinat position of
the Perendicular, which is sometimes expressed by cathetology, in­
structing us how it should be demitted, of [GREEK], and [GREEK], from 
[GREEK], pono, colloco.


Cathetoverticall,  is said of the Concordances of Loxogonosphericall
Moods in the Datas of the perpendicular, and the verticall Angle in 
the last operation.


Catoptrick,  the Science of perspective, from [GREEK], perspicio,
cerno.


Characteristick,  is said of the letters, which are the notes and marks
of distinction, called sometimes figuratives, or determinators, from
[GREEK], sculpo, imprimo.




Circles, great circles  are those which bisect the Sphere, lesser Circles those
which not.


Circular parts,  are in opposition to the reall and naturall parts of a Tri­
angle.


Circumjacent,  things which lie about, of circum, and jaceo.


Coalescencie,  a growing together, a compacting of two things in one; it
is said of the last two operations of the Loxogonosphericals conflated
into one, from coalesco or coaleo, of con and alo.


Cobase,  a fellow Base, or that which with another Base hath a common
Perpendicular, of con and basis.


Cocathetopposite,  is said of two, Angles at the Base, opposite to one
and the same Cathetos.


Coincidence,  a falling together upon the same thing, from coincido, of
con, and incido, ex in & cado.


Comment,  is an interpretation, or exposition of a thing, and comes from
comminiscor, comminisci, mentionem facere.


Compacted,  joyned, and knit together, put in one; from compingo,
compegi, compactum, vide Coalescencie.


Complement,  signifieth the perfecting that which a thing wanteth,
and usually is that, which an Angle or a Side wanteth of a Quadrant,
or 90. degrees: and of a Semicircle, or 180. from compleo, complere,
to fill up.


Concurse,  is the meeting of lines, or of the sides of a Triangle, from con­
curro, concursum.


Conflated,  compacted, joyned together, from conflo, conflatum , con­
flare, to blow together, vide Inchased.


Confectary,  is taken here for a Corollary, or rather a secondary Axiome,
which dependeth on a prime one, & being deduced from it, doth necessari­
ly follow, From consector, consectaris, the frequentative of consequor.


Consound,  to sound with another thing; it is said of consonants, which
have no vocality without the help of the vowell.


Constitutive,  is said of those things, which help to frame, make, and 
build up: from constituo, of con and statuo.


Constitutive sides,  the ingredient sides of a Triangle.


Constructive parts,  are those, whereof a thing is built, and framed: From
construo, constructum, to heap together, and build up, of con and
strues.


Conterminall,  is that which bordereth with, and joyneth to a thing, of



con and terminus, vide Adjacent, or Insident.


Cordes, and cordall,  are said of subtenses metaphorically; because the
Arches and subtenses are as the bow and string; chorda, comes of
the Greek word [GREEK], intestinum, illa, quia ex illis chordæ con­
ficiuntur.


Correctangle,  that is on which, with another rectangle, hath a common
Perpendicular.


Correspondent,  that which answereth with, and hath a reference to a­
nother thing, of con and respondeo.


Consinocosinall,  is said of the Concordances of Loxogonosphericall
Moods, agreeing, in that the termes of their finall Resolvers run upon
Consines.


Cosmography,  is taken here for the Science whereby is described the 
celestiall Globe, of [GREEK] and [GREEK].


Consubtendent,  is the subtendent of a correctangle, or that which with
another is substerned to two right Angles, made by the demission of
one and the same Perpendicular.


Coverticall,  is the fellow top Angle, from whence the Perpendicualar
falleth.


D.

DAta,  is said of the parts of a Triangle, which are given us, whe­
ther they be sides or Angles, or both, of do, datum, dare.


Datimista,  are those Datas, which are neither Angles onely, nor sides
onely, but Angles, and sides intermixedly: of data, and mista, from
misceo.


Datangulary,  is said of the Concordances of those Moods, for the ob­
taining of whose Prænoscendas, we have no other Datas, but An­
gles, unto the foresaid Moods common.


Datapurall,  comes from datapura, which be those Datas, that are
either meerly Angles, or meerly sides.


Datolaterall,  is said of the Concordances of those Moods, for the obtai­
ning of whose Prænoscendas, the same sides serve for Datas.


Datoquære,  is the very Problem it selfe, wherein two or three things are
given, and a third or forth required, as by the composition of the word
appears.


Datisterurgetick,  is said of those Moods which agree in the Datas of 
the last work: of data [GREEK], -postremum, and [GREEK], opus.




Demission,  is the letting fall of the Perpendicular: from demitto; de­
missum.


Determinater,  is the characteristick or figurative letter of a directory:
from determinare, to prescribe and limit.


Diagonall, taken substantively, or diagonie,  is a line drawn from one 
Angle to another, of [GREEK] and [GREEK] what the diagonie is in surfaces,
the axle is in solids.


Diagrammatise,  to make a Scheme or Diagram, from [GREEK], de­
lineo.


Diatyposis,  is a briefe summary desciption, and delineation of a
thing: or the couching of a great deale of matter, for the in­
struction of the Reader, in very little bounds, and in a most neat and
convenient order: from [GREEK], instituo, item melius dispono,
vide [GREEK].


Diodot,  is Pythagorases Bucarnon, or the gift bestowed on him by
the gods: of [GREEK], the genitive of [GREEK], and [GREEK], datus, from [GREEK],
do, vide Bucarnon.


Dioptrick,  the art of taking heights and distances, from [GREEK]
pervidendo, altitudinem dimensionemque turrium & murorum
exploro.


Directly,  is said of two rowes of proportionals, where the first terms
of the first row, is to the first of the second, as the last of the first,
is to the last of the second.


Directory,  is that which pointeth out the Moods dependent on an
Axiome.


Discrepant,  different, dissonant, id est, diverso modo crepare.


Disergeticks,  of two operations, of [GREEK], and [GREEK].


Document,  instruction, from doceo.


E.

ELucidation,  a clearing, explaining, resolving of a doubt, and com­
menting on some obscure passage, from elucido, elucidare.


Energie,  efficacie, power, force; from [GREEK], qui in opere est, of [GREEK] and
[GREEK], opus.


Enodandum,  that which is to be resolved and explicated, declared, and
made manifest, from enodo, enodare, to unknit, or cur away the
knot.




Equation, or rather æquation,  a making equall, from æquo, æquare.


Equiangularity,  is that affection of Triangles, whereby their Angles are
equall.


Equicrurall,  is said of Triangles, whose legs or shanks are equall; of
æquale, and crus, cruris; leg being taken here for the thigh and leg.


Equilaterall,  is said of Triangles, which have all their sides, shanks,
or legs equall, of æquus and polleo.


Equisolea, and Equisolearie,  are said of the grand Orthogono sphericall
Scheme; because of the resemblance it hath with a horse-shooe, and 
may in that sense be to this purpose applied with the same metaphori­
call congruencie, whereby it is said, that the royall army at Edge-hill
was imbatteled in a half-moon.


Equivalent,  of as much worth and vertue, of æquus and valeo.


Erected,  is said of Perpendicular, which are set or raised upright upon
a Base, from erigere, to raise up, or set aloft.


Externall,  extrinsecall,  exteriour, outward, or outer, are said oftest of
Angles, which being without the Area of a Triangle, are comprehen­
ded by two of its shanks meeting or cutting one another, accordingly as
one or both of them are protracted beyond the extent of the figure.


F.

FAciendas,  are the things which are to be done: faciendum is the ge­
rund of facio.


Figurative,  is the same thing as Characteristick, and is applied to those
letters which doe figure and point us out a resemblance and distinction
in the Moods.


Figures,  are taken here for those partitions of Trigonometry, which are
divided into Moods.

Flat,  is said of obtuse, or blunt Angles.


Forwardly,  is said of Analogies, progressive from the first terme to the
last.


Fundamentall,  is said of reasons, taken from the first grounds and prin­
ciples of a Science.




G.

Geodesie,  the Art of Surveying, of [GREEK], or [GREEK], terra, and [GREEK], divi­
do, partior.


Geography,  the Science of the Terrestriall Globe, of [GREEK] terra, and [GREEK],
describo.


Glosse,  signifieth a Commentary, or explication, it cometh from [GREEK]


Gnomon,  is a Figure lesse then the totall square, by the square of a Seg­
ment: or, according to Ramus, a Figure composed of the two supple­
ments, and one of the Diagonall squares of a Quadrat.


Gnomonick,  the Art of Dyalling, from [GREEK], the cock of a Dyall.


Great Circles,  vide Circles.


H.

HOmogeneall, and Homogeneity,  are said of Angles of the same
kind, nature, quality, or affection: from [GREEK], communio
generis.


Homologall,  is said of sides congruall , correspondent, and agreeable,
viz. such as have the same reason or proportion from [GREEK], si­
milis ratio.


Hypobasall,  is said of the Concordances of those Loxogonosphericall
Moods, which, when the Perpendicular is demitted, have for the Da­
tas of their second operation the same Subtendent and Base.


Hypocathetall,  is said of those which for the Datas of their third ope­
ration have the same Subtendent sides, from [GREEK] and [GREEK].


Hypotenusall,  is said of Subtendent and Perpendicular.


Hypotyposis,  a laying downe of severall things before our eyes at one
time, from [GREEK], oculis subjicio, delineo, & repræsento, vide
[GREEK].


Hypoverticall,  is said of Moods, agreeing in the same Catheteuretick
Datas of subtendent and verticall, as the Analysis of the word doth
shew.
 

I.

IDentity,  a samenesse, from idem, the same.


Illatitious, or illative,  is said of the terme which bringeth in the quæ­
situm, from infero, illatum.




Inchased, coagulated, fixed in, compacted, or conflated,  is said of the last
two Loxogonosphericall operations put into one, vide Compacted,
Conflated, and Coalescencie.


Including sides,  are the containing sides of an Angle of what affection
soever it be, vide, Ambients, Legs, &.


Individuated,  brought to the lowest division, vide, Specialised, and Spe­
cification.


Indowed,  is said of the termes of an Analogie, whether sides, or An­
gles, as they stand affected with Sines, Tangents, Secants, or their com­
plements, vide Invested.


Ingredient,  is that which entreth into the composition of a Triangle, or
the progresse of an operation, from ingredior, of in and gradior.


Initiall,  that which belongeth to the beginning, from initium, ab ineo,
significante incipio.


Insident,  is said of Angles, from insideo, vide Adjacent, or Conter­
minall.


Interjacent,  lying betwixt, of inter and jaceo; it is said of the Side or An­
gle betweene.


Intermediat,  is said of the middle termes of a proportion.


Inversionall,  is said of the Concordances of those Moods which agree in 
the manner of their inversion; that is in placing the second and fourth
termes of the Analogy, together with their indowments, in the roomes
of the first and third, and contrariwise.


Invested,  is the same as indowed, from investio, investire.


Irrationall,  are those which are commonly called sard numbers, and are
inexplicable by any number whatsoever, whether whole, or broken.


Isosceles,  is the Greek word of equicturall, of [GREEK], [GREEK], and [GREEK], cros.


L.

LAterall,  belonging to the sides of a Triangle, from latus, lateris.


Leg,  is one of the including sides of an Angle, two sides of every
Triangle being called the Legs, and the third, the Base; the Legs
therefore or shankes of an Angle are the bounds insisting or standing
upon the base of the Angle.


Line of interception,  is the difference betwixt the Secant, and the Radi­
us, and is commonly called the residuum.


Logarithms,  are those artificiall numbers, by which, with addition and



subtraction onely, we work the same effects, as by other numbers, with
multiplication and division: of [GREEK], ratio, proportio, and [GREEK], nu­
merus.


Logarithmication,  is the working of an Analogy by Logarithms, with­
out having regard to the old laborious way of the naturall Sines, and
Tangents; we say likewise Logarithmicall and Logarithmically, for
Logarithmeticall and Logarithmetically; for by the syncopising of et;
the pronunciation of those words is made to the eare more pleasant: a
priviledge warranted by all the dialects of the Greek, and other the
most refined Languages in the world.


Loxogonosphericall,  is said of oblique sphericals, or [GREEK], obliquus,
and [GREEK], ad sphæram pertinens, from [GREEK], globus.


M.

MAjor and Minor Arches,  vide Arch.


Maxim, an axiome, or principle,  called so ( from maximus ) be­
cause it is of greatest account in an Art of Science, and the principall
thing we ought to know.


Meane, or middle proportion,  is that, the square whereof is equall to the
plane of the extremes: and called so because of its situation in the 
Analogy.


Mensurator,  is that, whereby the illatitious terme is compared, or mea­
sured with the maine quæsitum.


Monotropall,  is said of figures, which have one onely Mood, of [GREEK],
and [GREEK], from [GREEK].


Monurgeticks,  are said of those Moods, the maine Quæsitas whereof
are obtained by one operation, of [GREEK], and [GREEK].


Moods,  determine unto us the severall manners of Triangles, from mo­
dus, a way, or manner.


N.

NAturall,  the naturall parts of a Triangle, are those of which it is
compounded, and the circular, those whereby the maine quæsi­
tum is found out.


Nearest, or next,  is said of that Cathetopposite Angle, which is imme­
diatly opposite to the pendendicular.




Notandum,  is set downe for an admonition to the Reader, of some re­
markable thing to follow, and is the gerund of Noto, notare.


O.

OBlique, and obliquangulary,  are said of all Angles that are not
right.


Oblong,  is a parallelogram, of square more long then large: from ob­
longus, very long.


Obtuse, and obtuse angled,  are said of flat, and blunt Angles.


Occurse,  is a meeting together, from occurio, occurium.


Oppobasall,  is said of those Moods, which have a Cathereuretick Con­
cordance in their Datas of the same Cathetopposite Angles, and the 
same Bases.


Oppocatherall,  is said of those Loxogonosphericals which have a Da­
tisterurgetick Concordance in their Datas of the same Angles at
the Base, and the Perpendicular.


Oppoverticall,  is said of those Moods which have a Catheteuretick
Concordance in their Datas of the same Cathetopposites, and verticall
Angles.


Orthogonosphericall,  is said of right angled Sphericals, of [GREEK],
[GREEK], [GREEK], angulus, and [GREEK], globus.


Oxygonosphericall,  is said of acute-angled sphericals, of [GREEK], [GREEK],
and [GREEK].


P.

Parallelisme,  is a Parallel, equality of right lines, cut with a right
line, or of Sphericals with a Sphericall, from [GREEK], equidi­
stans of [GREEK], and [GREEK].


Parallelogram,  is an oblong, long square, rectangle, or figure made of
parallel lines: of [GREEK], and [GREEK], linea.


Partiall,  is said of enodandas depending on severall Axioms.


Particularise,  specialise, by some especiall difference to contract the gene­
rality of a thing.


Partition,  is said of the severall operations of every Loxogonosphericall
Mood, and is divided in prænoscendall, catheteuretick and hysterur­
getick.


Permutat proportion, or proportion by permutation, or alternat proporti­



on,  is when the Antecedent is compared to the Antecedent, and the Con­
sequent to the Consequent, vide, Perturbat.


Perpendicularity,  is the affection of the Perpendicular, or plumb-line;
which comes from perpendendo, id est, explorando altitudinem.


Perturbat,  is the same as permutat, and called so because the order of
the Analogie is perturbed.


Planobiquangular,  is said of plaine Triangles, where in there is no right
Angle at all.


Planorectangular,  is said of plaine right-angled Triangles.


Planotriangular,  is said of plaine Triangles, that is, such as are not
Sphericall.


Pleuseotechnie,  the Art of Navigation, of [GREEK], [GREEK], naviga­
tio, and [GREEK] ars.


Plusminused,  is said of Moods which admit of Mensurators or whose
illatitious termes are never the same, but either more or lesse then the
maine quæntas.


Poltechyrologie,  the Art of fortifying Townes and Cities, of [GREEK],
urbs, civitas [GREEK], munio firmo, and [GREEK], ratio.


Possubservient,  is that which after another serveth for the resolving of
a question; of posi and subserviens; of sub and servio.


Potentia,  is that wherein the force and whole result of another thing lies.


Power,  is the square, quadrant , or product of a line extended upon it selfe,
or of a number in it selfe multiplied.


Powered,  squared quadrified.


Precept,  document, from præcipio, præceptum.


Prænoscenda,  are the termes, which must be knowne before we can at­
taine to the knowledge of the maine quasitas: of præ and nosco.


Prænoscendall,  is said of the Concordances of those Moods, which a­
gree in the same prænoscendas.


Præfection, præfectionall,  is concerning the digit towards the left, whose 
cutting off saveth the labour of subtracting the double or single Ra­
dius.


Præscinded problems,  are those speculative Datoquæres, which are not
applied to any matter by way of practice.


Præsubservient,  is said of those Moods which in the first place we must
make use of for the explanation of others; of præ, and subiervio.


Prime,  is said of the furthest Cathetopposite, or Angle at the Base, con­
tained within the Triangle to be resolved.




Primifie the Radius,  is to put the Radius in the first place, primum­
que inter terminus collocare proportionales.


Problem, problemet,  a question or datoquære, from [GREEK], unde
[GREEK], propositum, objectaculum.


Product,  is the result, factus, or operatum of a multiplication, from
produco, productum.


Proportion, proportionality,  are the same as Analogy, and Analogisme;
the first being a likenesse of termes, the other of proportions.


Proposition,  a proposed sentence, whether theorem or problem.


Prosiliencie,  is a demission, or falling of the Perpendicular, from pro­
silio, ex pro & salio.


Proturgetick,  is said of the first operation of every Disergetick Mood,
of [GREEK], and [GREEK], the [GREEK] being Attically contracted into [GREEK].


Q.

QUadrant,  the fourth part of a Circle.


Quadranting,  the protracting of a Sphericall side unto a Qua­
drant.


Quadrat,  a Square, a forma quadræ, the power or possibility of a line,
vide, Power.


Quadrobiquadræquation,  concerneth the Square of the subtendent
side, which is equall to the Biquadrat, or two Squares of the Am­
bients.


Quadrosubduction,  is concerning the subtracting of the Square of 
one of the Ambients from the Square of the Subtendent.


Quæsitas,  the things demanded from quæro, quæsitum.


Quotient,  is the result of a division, from quoties, how many times.


R.

RAdicaly meeting,  is said of those Oblongs, or Squares, whose
sides doe meet together.


Radius, ray or beame  is the Semidiameter, called so metaphorically, from
the spoake of a wheele which is to the limb thereof, as the Semidiame­
ter, to the circumference of a circle.


Reciprocall,  is said of the proportionalities, or two rowes of proportionals,
wherein the first of the first is to the first of the second, as the last of



the second is to the last of the first, and contrarily.


Rectangular,  is said of those figures, which have right Angles.


Refinedly,  is said when we go the shortest way to work by primifying the 
Radius.


Renvoy,  a remitting from one place to another, it comes from the French
word Renvoyer.


Representative,  is said of the letters, which stand for whole words; as
E. for side, L. for secant, U. for subtendent.


Residuat,  is to leave a remainder, nempe id quod resider & superest.


Resolver,  is that which looseth and untieth the knot of a difficulty, of re
and solvo.


Resolutory,  is said of the last partition of the Loxogonosphericall opera­
tions.


Result,  is the last effect of a work.


Root,  is the side of a Square, Cube, or any cossick figure.


S.

SCheme,  signifieth here the delineation of a Geometricall figure, with
all parts necessary for the illustrating of a demonstration, from [GREEK],
habeo.


Sciography,  the Art of shadowing, of [GREEK], umbra, and [GREEK], scribo.


Segment,  the portion of a thing cut off, quasi secamentum, quod a re
aliqua secatur.


Sexagesimat, subsexagesimat, resubsexagesimat, and biresubsexagesi­
mat,  are said of the division, subdivision, resubdivision, and reer-resub­
division of a degrees into minuts, seconds, thirds, and fourths in 60.
of each other: the devisor of the fore goer being successively the fol­
lowing dividend, and the quotient always sixty.

Sharp,  is said of acute Angles.


Sindiforall,  is said of those Moods, the fourth terme of whose Analogie
is onely illatitious to the maine quæsitum.


Sindiforation,  is the affection of those foresaid Moods, whereby the va­
lue of the mensurator is knowne.


 Sindiforatall,  is concerning those Moods, whose illatitious terme is an
Angle.


Sindiforiutall,  is of those Moods, whose illatitious terme is a side: all
these foure words are composed of representatives, and ( if I remember
well) mentioned in my explanation.




Sinocosinall,  is said of the Concordances of those Moods, which agree in 
this, that their Analogies run upon sines, and sine-complements.


Sinocotangentall,  is said of those Moods, which agree in that the termes
of their Analogie run upon Sines and Tangent-complements.


Sinus,  is so called ( I believe ) because it is alwayes in the very bosome of
the Circle.


Sinused,  is said of termes endowed or invested with Sines.


Specialized,  contracted to more particular termes, vide, Individuated.


Specifying,  determinating particularising.


Specification,  a making more especiall, by contracting the generality of
a thing, vide, Specialized.


Sphericodisergeticks,  are the Sphericall Triangles of two operations.


Structure of an operation,  is the whole frame thereof, from struo, stru­
ctum.


Subdatoquære,  is a particular datoquære, and is applied to the pro­
blems of the cases of every Sphericodisergetick Mood, vide, Sub-pro­
blems.


Subajcent,  is the substerned side or the Base, of sub & jaceo, vide, Su­
stentative, Sustaining side and Substerned.


Subordinate problems,  is the same with subdatoquære.


Subproblems,  is the same with subordinate problems, or problemets.


Subservient,  is said of Moods which serve in the operation of other 
Moods.


Substerned,  is the subjacent side of Base: or, more generally, and side
opposite to an Angle: of sub and sterno, sternere, vide, Sub­
jacent.


Subtendent,  is the side opposite to the right Angle, of sub and tendo:
as if you would say, Under-stretched.


Subtendentine,  is the subtendent of a little rectangled Triangle, com­
prehended within the Area of a great one, and is sometimes called the
little subtendent, and reere subtendent.


Subtendentall,  is the subtendent of a great rectangled Triangle, within
whose capacity is included a little one: it is likewise called the great
subtendent, and maine subtendent.


Supernumerary,  is said of the digit, by the which the proposed number
exceeds in places the number of the places of the Radius.


Supplements,  are the Oblongs made of the Segments of the root of a 
Square; and so called, because they supply all that the Diagonals or



Squares of the Segments joyned together, want of the whole lines
square.


Suppone severally,  is to signifie severall things.


Sustaining side  is the substerned, or subjacent side.


Sustentative,  is the same with sustaining, substerned, subjacent and
Base.


Sympathie of Angles,  is a similitude in their affection, of [GREEK], and 
[GREEK], passio, vide homogeneall.


T.

TAble,  is an Index sometimes, and sometimes it is taken for a
Briefe and summary way of expessing many things.


Tangentine,  is that which concerneth Tangents or touch-lines.


Tangentosinall,  is said of the Concordance of those Loxogonosphe­
ricals, the termes of whose Analogie runne upon Tangents and
Sines.


Tenet,  is a secondary maxim, and is onely said here of Catheto­
tetick principles.


Theorematick,  speculative, from [GREEK], a speculation, which com­
eth from [GREEK], or [GREEK], speculare, or contemplare.


Topanglet, and verticalin  are the same.


Trigonometry,  is the Art of calculating, and measuring of Triangles
of [GREEK], triangulus, and [GREEK], metior.


Trislotetras,  is that which runneth all upon threes and foures
of [GREEK], and in plurali, [GREEK], tertius, trinus, triplex, tres, and
[GREEK], numerus quaternarius, from [GREEK], quatuor.


U.

VAriator,  is from vario, variare, to diversifie, and is said of cases,
which upon the same Datas are onely diverse in the manner of re­
solving the quæsitum.




Verticaline, verticall, verticalet,  are the top angles, and top anglets, from
vertex, verticis.


Underproblem, problemet, subordinate problem, sub-problem, under-da­
roquæere, and sub. datoquære  are, all the same thing.


Unradiated, or unradiused,  is said of a summe of Logarithms from
which the Radius is abstracted.


Z.

ZEterick,  is said of Loxogonosphericall Moods which agree in
the same quæsitas, from [GREEK], quæro, inquiro.