Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	angle_n	line_n	right_a	2,182	5	9.6733	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A95751	The trissotetras: or, a most exquisite table for resolving all manner of triangles, whether plaine or sphericall, rectangular or obliquangular, with greater facility, then ever hitherto hath been practised: most necessary for all such as would attaine to the exact knowledge of fortification, dyaling, navigation, surveying, architecture, the art of shadowing, taking of heights, and distances, the use of both the globes, perspective, the skill of making the maps, the theory of the planets, the calculating of their motions, and of all other astronomicall computations whatsoever. Now lately invented, and perfected, explained, commented on, and with all possible brevity, and perspicuity, in the hiddest, and most re-searched mysteries, from the very first grounds of the science it selfe, proved, and convincingly demonstrated. / By Sir Thomas Urquhart of Cromartie Knight. Published for the benefit of those that are mathematically affected.	Urquhart, Thomas, Sir, 1611-1660.	1645 (1645)	Wing U140; Thomason E273_9; ESTC R212170	85,776	129

certain all Magnitudes being Figures at least in power and all Figures either Triangles or Triangled that the Arithmeticall Solution of any Geometricall question dependeth on the Doctrine of Triangles 5. And though the proportion betwixt the parts of a Triangle cannot be without some errour because of crooked lines to right lines and of crooked lines amongst themselves the reason is inscrutable no man being able to finde out the exact proportion of the Diameter to the Circumference yet both in plain Triangles where the measure of the Angles is of a different species from the sides and in Sphericalls wherein both the Angles and sides are of a circular nature crooked lines are in some measure reduced to right lines by the definition of quantity which right lines viz. Sines Tangents and Secants applyed to a Circle have in respect of the Radius o● half-Diameter 6. And therefore though the Circles Quadrature be not found out it being in our power to make the Diameter or the semi-Diameter which is the Radius of as many parts as we please and being sure so much the more that the Radius be taken the error will be the lesser for albeit the Sines Tangents and Secants be irrationall thereto for the most part and their proportion inexplicable by any number whatsoever whither whole or broken yet if they be rightly made they will be such as that in them all no number will be different from the truth by an integer or unity of those parts whereof the Radius is taken which is so exactly done by some especially by Petiscus who assumed a Radius of twenty six places that according to his supputation the Diameter of the Earth being known and the Globe thereof supposed to be perfectly round one should not fail in the dimension of its whole Circuit the nine hundreth thousand scantling of the Million part of an Inch and yet not be able for all that to measure it without amisse for so indivisible the truth of a thing is that come you never so neer it unlesse you hit upon it just to a point there is an errour still DEFINITIONS A Cord or Subtense is a right line drawn from the one extremity 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 Angles 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 Logarithmicall calculations they are altogether uselesse and therefore in my Trissotetras there is no mention made of them 8. In Amblygonosphericall● which admit both of an Extrinsecall and Intrinsecall demission of the perpendicular nineteen severall parts are to be considered viz. The Perpendicular the Subtendentall the Subtendentine two Cosubtendents the Basall the Basidion the chief Segment of the Base two Cobases the double Verticall the Verticall the Verticaline two Coverticalls the next Cathetopposite the prime Cathetopposite and the two Cocathetopposites fourteen whereof to wit the Subtendentall the Subtendentine the Cosubtendents the Basall the Basidion the Cobases the Verticall the Verticaline the Coverticalls and Cocathetopposites are called the first either Subtendent Base Topangle or Cocathetopposite whither in the great Triangle or the little or in the Correctangle if they be ingredients of that Rectangular whereof most parts are known which parts are alwayes a Subtendent and a Cathetopposite 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 Perpendicular and Subtendentall and divided by the Subtendentine the internall is included by cosubtendents and divided by the Perpendicular APODICTICKS THe Angles made by a right Line falling on another right Line are equall to two right Angles because every Angle being measured by an Arch or part of a Circumference and a right Angle by ninety Degrees if upon the middle of the ground line as Center be described a semi-Circle it will be the measure of the Angles comprehended betwixt the falling and sustaining lines 2. Hence it is that the four opposite Angles made by one line crossing another are always each to its own opposite equall for if upon the point of Intersection as Center be described a Circle every two of those Angles will fill up the semi-Circle therefore the first and second will be equall to the second and third and consequently the second which is the common Angle to both these couples being removed the first will remain equall to the third and by the same reason the second to the fourth which was to be demonstrated 3. If a right line falling upon two other right lines make the alternat Angles equall these lines must needs be Paralell for if they did meet the alternat Angles would not be equall because in all plain Triangles the outward Angle is greater then any of the remote inward Angles which is proved by the first 4. If one of the sides of a Triangle be produced the outward Angle is equall to both the inner and opposite Angles together because according to the acclining or declining of the conterminall side is left an Angulary space for the receiving of a paralell to the opposite side in the point of whose occourse at the base the Exterior Angle is divided into two which for their like and alternat situation with the two Interior Angles are equall each to its own conform to the nature of Angles made by a right line crossing divers paralells 5. From hence we gather that the three Angles of a plain Triangle are equall to two rights for the two inward being equall to the Externall one and there remaining of the three but one which was proved in the first Apodictick to be the Externall Angles complement to two rights it must needs fall forth what are equall to a third being equall amongst themselves that the three Angles of a plain Triangle are equall to two right Angles the which we undertook to prove 6. By the same reason the two acute of a Rectangled plain Triangle are equall to one right Angle and any one of them the others complement thereto 7.

In every Circle an Angle from the Center is two in the Limb both of them having one part of the Circumference for base for being an Externall Angle and consequently equall to both the Intrinsecall Angles and therefore equall to one another because of their being subtended by equall bases viz. the semi-Diameters it must needs be the double of the foresaid Angle in the limb 8. Triangles standing between two paralells upon one and the fame base are equall for the Identity of the base whereon they are seated together with the Equidistance of the Lines within the which they are confined maketh them of such a nature that how long so ever the line paralell to the base be protracted the Diagonall cutting of in one off the Triangles as much of bredth as it gains of length the ones losse accruing to the profit of the other Quantifies them both to an equality the thing we did intend to prove 9. Hence do we inferre that Triangles betwixt two paralells are in the same proportion with their bases 10. Therefore if in a Triangle be drawn a paralell to any of the sides it divideth the other sides through which it passeth proportionally for besides that it maketh the four segments to be four bases it becomes if two Diagonall lines be extended from the ends thereof to the ends of its paralell a common base to two equall Triangles to which two the Triangle of the first two segments having reference according to the difference of their bases and these two being equall as it is to the one so must it be to the other and therefore the first base must be to the second which are the Segments of one side of the Triangle as the third to the fourth which are the Segments of the second all which was to be demonstrated 11. From hence do we collect that Equiangled Triangles have their sides about the equall Angles proportionall to one another This sayes Petiscus is the golden Foundation and chief ground of Trigonometry 12. An Angle in a semi-Circle is right because it is equall to both the Angles at the base which by cutting the Diameter in two is perceivable to any 13. Of four proportionall lines the Rectangled figure made of the two extreames is equall to the Rectangular composed of the means for as four and one are equall to two and three by an Arithmeticall proportion and the fourth term Geometrically exceeding or being lesse then the third as the second is more or lesse then the first what the fourth hath or wanteth from and above the third is supplyed or impaired by the Surplusage or deficiency of the first from and above the second These Analogies being still taken in a Geometricall way make the oblong of the two middle equall to that of the extreams which was to be proved 14. In all plain Rectangled Triangles the Ambients are equall in power to the Subtendent for by demitting from the right Angle a Perpendicular there will arise two Correctangles from whose Equiangularity with the great Rectangle will proceed such a proportion amongst the Homologall sides of all the three that if you set them right in the rule beginning your Analogy at the main Subtendent seeing the including sides of the totall Rectangle prove Subtendents in the partiall Correctangles and the bases of those Rectanglets the Segments of the great Subtendent it will fall out that as the main Subtendent is to his base on either side for either of the legs of a Rectangled Triangle in reference to one another is both base and Perpendicular so the same bases which are Subtendents in the lesser Rectangles are to their bases the Segment of the prime Subtendent Then by the Golden rule we find that the multiplying of the middle termes which is nothing else but the squaring of the comprehending sides of the prime Rectangular affords two products equall to the oblongs made of the great Subtendent and his respective Segments the aggregat whereof by equation is the same with the square of the chief Subtendent or Hypotenusa which was to be demonstrated 15. In every totall square the supplements about the partiall and Interior squares are equall the one to the other for by drawing a Diagonall line the great square being divided into two equall Triangles because of their standing on equall bases betwixt two paralells by the ninth Apodictick it is evident that in either of these great Triangles there being two partiall ones equall to the two of the other each to his own by the same Reason of the ninth If from equall things viz. the totall Triangles be taken equall things to wit the two pairs of partiall Triangles equall things must needs remain which are the foresaid supplements whose equality I undertook to prove 16. If a right line cut into two equall parts be increased the square made of the additonall line and one of the Bisegments joyned in one lesse by the Square of the half of the line Bisected is equall to the oblong contained under the prolonged line and the line of Continuation for if annexedly to the longest side of the proposed oblong be described the foresaid Square there will jet out beyond the Quadrat Figure a space or Rectangle which for being powered by the Bisegment and Additionall line will be equall to the neerest supplement and consequently to the other the equality of supplements being proved by the last Apodictick by vertue whereof a Gnomon in the great Square lacking nothing of its whole Area but the space of the square of the Bisected line is apparent to equalize the Parallelogram proposed which was to be demonstrated 17. From hence proceedeth this Sequell that if from any point without a circle two lines cutting it be protracted to the other extremity thereof making two cords the oblongs contained under the totall lines and the excesse of the Subtenses are equall one to another for whether any of the lines passe through the Center or not if the Subtenses be Bisected seeing all lines from the Center fall Perpendicularly upon the Chordall point of Bisection because the two semi-Diameters and Bisegments substerned under equall Angles in two Triangles evince the equality of the third Angle to the third by the fift Apodictick which two Angles being made by the falling of one right line upon another must needs be right by the tenth definition of the first of Euchilde the Bucarnon of Pythagoras demonstrated in my fourteenth Apodictick will by Quadrosubductions of Ambients from one another and their Quadrobiquadrequation● with the Hypotenusa together with other Analogies of equation with the powers of like Rectangular Triangles comprehended within the same circle manifest the equality of long Squares or oblongs Radically meeting in an Exterior point and made of the prolonged Subtenses and the lines of interception betwixt the limb of the circle and the point of concourse quod probandum fuit 18. Now to look back on the eleaventh Apodictick where according to Petiscus

I said that upon the mutuall proportion of the sides of Equiangled Triangles is founded the whole Science of Trigonometry I do here respeak it and with confidence maintain the truth thereof because besides many others it is the ground of these Subsequent Theorems 1. The right sine of an Arch is to its co-sine as the Radius to the co-tangent of the said Arch. 2. The co-sine of an Arch is to its sine as the Radius to the Tangent of the said Arch. 3. The Sines and co-Secants the Secants and co-Sines and the Tangents and co-Tangents are reciprocally proportionall 4. The Radius is a mean proportionall betwixt the Sine and co-Secant the Secant and co-Sine and the Tangent and co-Tangent The verity of all these If a Quadrant be described and upon the two Radiuses two Tangents and two or three Sines be erected which in respect of other Arches will be co-Sines and co-Tangents and two Secants drawn which are likewise co-Secants from the Center to the top of the Tangents will appear by the foresaid reasons out of my eleaventh Apodictick The Trissotetras Plain Sphericall Plain Trissotetras Axiomes four 1. Rulerst Vradesso Directory Enodandas Eradetul Vphechet 3. Orth. 1. Obl. 2. Eproso Directorie Enodandas 3. Ax. Grediftal Dir. ● Pubkegdaxesh 4. Orth. 4. Ax. Bagrediffiu Dir. ● 3. Obl. The Planorectangular Table Figures four 1. Va* le Datas Quaesitas Resolvers Vp* Al§em Rad V Sapy ☞ Yr. 2. Ve* mane Vb* em §an V Rad Eg ☞ So.   Praesubserv Possubserv Vph* en §er Vb* em §an Vp* al§em or Eg* al§em 3. Ena* ve Ek* ar §ul Sapeg Eg Rad ☞ Vr Eg* al §em Rad Taxeg Eg ☞ Yr.     Praesubserv Possubserv 4. Ere* va Ech* em §un Et* en §ar Ek* ar §ul Et* en §ar E Ge Rad ☞ Toge The Planobliquangular Table Figures four 1. Alahe * me Da*na*re §le Sapeg Eg Sapyr ☞ Yr. 2. Emena*role The*re* lab §mo Aggres Zes Talfagros ☞ Talzo   Praesubserv Possubserv Ze*le*mab §ne The*re* lab §mo Da*na*re §le 3. Enero*lome Xe* me* no §ro E So Ge ☞ So.     Praesubserv Possubserv She*ne* ro §lem Xe* me* no §ro Da*na*re §le     Praesubserv Possubserv 4. Erele* a Pse* re* le §ma Bagreziu Vb*em §an Finall Resolver Vxi●q Rad 〈◊〉 ☞ Sor. The Sphericall Trissotetras Axiomes three 1. Suprosca Dir. uphugen 2. Sbaprotca pubkutethepsaler 3. Seproso uchedezexam The Orthogonospherical Table Figures 6. Datoquaeres 16.   Dat. Quaes Resolvers 1. Valam*menep Vp*al§am Torb Tag Nu ☞ Mir. Vb*am§en Nag Mu Torp ☞ Myr. or   Torp Mu Lag ☞ Myr. Vph*an §ep Tol Sag Su ☞ Syr. 2. Veman*nore Vk*el§amb Meg Torp Mu ☞ Nir. or   Torp Teg Mu ☞ Nir. Ug*em §on Su Seg Tom ☞ Sir or   Tom Seg Ru ☞ Sir Uch*en §er Neg To Nu ☞ Nyr or   To Le Nu ☞ Nyr 3. Enar*rulome Et*al§um Torp Me Nag ☞ Mur. Ed*am§on To Neg Sa ☞ Nir. Eth*an§er Torb Tag Se ☞ Tyr. 4. Erol*lumane Ez*●l§um Sag Sep Rad ☞ Sur. or   Rad Seg Rag ☞ Sur. Ex*●● §an Ne To Nag ☞ Sir or   To Le Nag ☞ Sir Eps* on §er Tag Tolb Te ☞ Syr. or   Tolb Mag Te ☞ Syr. 5. Acha* ve Al* am §un Tag Torb Ma ☞ Nur. or   Torb Mag Ma ☞ Nur. Am* an §er Say Nag T● ☞ Nyr or   Tω Noy Ray ☞ Nyr 6. Eshe*va En*er §ul Ton Neg Ne ☞ Nur. Er* el §am Sei Teg Torb ☞ Tir. or   Torb Tepi Rexi ☞ Tir. The Loxogonospherical Trissotetras Monurgetick Disergetick The Monurgetick Loxogonospherical Table Axiomes two 1. Seproso Dir. Lame Figures two 2. Parses Dir. Nera Moods four Figures Datas Quaes Resolvers 1. Datamista Lam*an*ep § rep Sapeg Se Sapy ☞ Syr. Me*ne*ro § lo. Sepag Sa Sepi ☞ Sir       ad 2. Datapura Ne*re*le § ma. Hal Basaldileg Sad Sab Re Regals Bis*ir     ab     Parses Powto Parsadsab ☞ PowsalvertiR Ra*la*ma § ne Kour Bfasines ereled Kouf Br*axypopyx The Loxogonospherical Disergeticks Axiomes foure 1. Na Bad prosver Dir. Alama 2. Naverpr or Tes. Allera 3. Siubpror Tab. Ammena 4. Niub prodesver Errenna Figures 4. Moods 8.   Fig. M. Sub Res Dat. Praen Cathetothesis Final Resolvers 1. Ab A         Cafregpiq     La Vp Tag ut * Op § At Dasimforaug Sat-nop-Seud † nob Kir A Meb Al Nu ud * Ob § Aud Dadisforeug Saud-nob-Sat † nop Ir.   Na. Am Mir uth* Oph § Auth Dadisgatin Sauth-noph-Seuth † nops Ir. Leb 2. Sub. Res Dat. P●ae● Cathetothesis Final Resolvers   Al         Cafyxegeq   Ma La Vp Tag ut * op § at dasimforauxy nat-mut-naud † mwd   Meb Al Nu ud * ob § aud dadiscracforeug naud-mud-nat † mwt Ne Ne Am Mir uth * oph § auth dadiscramgatin nauth-muth-neuth † mwth Fig. M.       Cathetothesis Plus minus A A Sub. Re. Dat. Pr. Cafriq Final Resolvers Sindifora                 At   Ma up Tag ut*Op § At Dadissepamforaur Nop-Sat-Nob ☞ Seudfr Autir Ha Nep Al Nu ud*Ob § Aud Dadissexamforeur Nob-Saud-Nop ☞ Satfr Eutir                 Aud   Ra Am Mir uth* Oph § Auth Dasimatin Noph-Seuth-Nops ☞ Soethj Authir Mep 4.       Cathetothesis Plus minus   Am Sub. Re. Dat. Pr. Cafregpagiq Final Resolvers Sindiforiu                 Aet Na Ma ub Mu Ut* Op § Aet Dadissepamfor Tob-Top-Saet ☞ Soedfr Dyr   Nep Am Lag Ud* Ob § Aed Dadissexamfor Top-Tob-Saed ☞ Soetfr Dyr                 Aed Re Reb En Myr Uth* Oph § aeth Dasimin Tops-Toph-SAEth ☞ Soethj aeth Syr. Fig. M. Cathetothesis Eb En Sub. Re. Dat. Pr. Cafregpigeq Final Resolvers   Er Ub Mu Ut* Op § aet Dacramfor Soed-Top-Saet ☞ Tob. Kir En Ab Am Lag Ud* Ob § ad Damracfor Soet-Tob-Saed ☞ Top. Ir.   Lo En Myr Uth* Oph § aeth Dasimquaein Soeth-Toph-Saeth ☞ Tops Ir. Ab 6. Cathetothesis   En Sub. Re. Dat. Q. Pr. Cafregpiq Final Resolvers Ro Ne Ub Mu ut* Op § aet Dacforamb Naet-Nut-Noed ☞ Nwd Yr.   Rab Am Lag ud* Ob § aed Damforac Naed-Nud-Noet ☞ Nwt Yr. Le Le En Myr uth* Oph § aeth Dakinatam Naeth-Nuth-Noeth ☞ Nwth Yr. Fig. M.         Cathteothesis Plus minus Eb E Sub. Re. Dat. Pr. Cafriq Final Resolvers Sindifora                 At   Re Up Tag Ut* Op § at Dacracforaur Mut-Nat-Mwd ☞ Neudfr Autir Er Lo Al Nu Ud* Ob § aud Dambracforeur Mud-Naud-Mwt ☞ Natfr Autir                 Aud   Mab Am Mir Uth* Oph § auth Dacrambatin Muth-Nauth-Mwth ☞ Neuthj Authir Om 8.         Cathetothesis Plus minus   Er Sub. Re. Dat. Pr. Cacurgyq

much worth and vertue of aequus and valeo Erected is said of Perpendiculars 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 comprehended 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 gerund 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 principles of a Science G. GEodesie the Art of Surveying of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 terra and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 divido partior Geography the Science of the Terrestriall Globe of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 terra and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 describo Glosse signifieth a Commentary or explication it cometh from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Gnomon is a Figure lesse then the totall square by the square of a Segment or according to Ramus a Figure composed of the two supplements and one of the Diagonall squares of a Quadrat Gnomonick the Art of Dyalling from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 communio generis Homologall is said of sides congruall correspondent and agreeable viz. such as have the same reason or proportion from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 similis ratio Hypobasall is said of the Concordances of those Loxogonosphericall Moods which when the Perpendicular is demitted have for the Datas of their second operation the same Subtendent and Base Hypocathetall is said of those which for the Datas of their third operation have the same Subtendent and Perpendicular Hypotenusall is said of Subtendent sides from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Hypotyposis a laying downe of severall things before our eyes at one time from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 oculis subjicio delineo repraesento vide 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 quaesitum 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 c. Individuated brought to the lowest division vide Specialised and Specification Indowed is said of the termes of an Analogie whether sides or Angles as they stand affected with Sines Tangents Secants or their complements 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 Conterminall Interjacent lying betwixt of inter and jaceo it is said of the Side or Angle 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 surd numbers and are inexplicable by any number whatsoever whether whole or broken Isosceles is the Greek word of equicrurall of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 crus 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 Radius 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ratio proportio and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 numerus Logarithmication is the working of an Analogy by Logarithms without 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 of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 obliquus and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ad sphaeram pertinens from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 globus M. MAjor and Minor Arches vide Arch. Maxim an axiome or principle called so from maximus because it is of greatest account in an Art or 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 measured with the maine quaesitum Monotropall is said of figures which have one onely Mood of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Monurgeticks are said of those Moods the maine Quaesitas whereof are obtained by one operation of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Moods aetermine unto us the severall manners of Triangles from modus 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 quaesitum is found out Nearest or next is said of that Cathetopposite Angle which is immediatly opposite to the perpendicular Notandum is set downe for an admonition to the Reader of some remarkable 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 or square more long them large from oblongus very long Obtuse and obtuse angled are said of