SUB
jga-j-^b— i\i 19 -fi — " — j«— \b-\- % —3 1 +2
[ 144 3
sue
3° If the Quantities have different Signs ; the Subpattion is converted into Addition, and to the Aggregate is prefix'd the Sign of the Quantity, whence the SubfixaBiwi is to be made : For Example ;
%a— $c + 9^ =8#£. — 5+9^ &a — %c — id =6 —8 — 7
2^ + 3 c-\-\6d=^ 2 lib. -\- 1 -\- 16
4 If the Quantities be exprefs'd in different Letters ; they muft be conneded ; only the Characters of the Subtrahend mull be changed into the contrary ones : For Example ;
a4-b — c d-e+f
ti+d c~e-g
d-^-b—c—d + e—f . a-]-d — c-\-e--g
Subtraction of logarithms y (Logarithm.
Substruction of F?t/gar FraffiionSf. See ^Fractions. Substraction of Decimals J (Decimals.
SUBSTRUCTION, in Building. See Foundation. SUBSTYLAR Line, in Dialling, a right Line, whereon the Style or Gnomon of a Dial is erected. See Gnomon. •
In Polar, Horizontal, Meridional and Northern Dials, the Subjtylar Line is the Meridian Line, or Line of 13, a Clock ; or the Interferon of the Plane, whereon the Dial is delineated, with that of the Meridian. See Meri- dian.
In Eafterly and Wefterly Dials, the Subjtylar Line, is the Line of Six a Clock; or the Intersection of the Plane, where- on the Dial is delineated, with the prime Vertical. See Dial.
SUB-TANGENT, of a Curve, is the Line that deter- mines the Interfcclion of the Tangent with the Axis ; or, that determines the Point wherein the Tangent cuts the Axis, pro- longed. See Curve.
Thus, in the Curve A M, fgc. (Tab. Analytkks, Fig. 10.) the Line T P intercepted between the Semiordinate P M, and the Tangent T M, is the Sub'tangent. And PR is to PM, asPMtoPT; andPMtoPT, as MR to TM.
'Tis a Rule in all Equations, that if the Value of the Sub-tangent come out poiitive, the Point of Interfe&ion of the Tangent and Axis, falls on that Side of the Ordinate, where the Vertex of the Curve lies ; as in the Parabola and Paraboloides.
If it come out Negative, the Point of Interferon will fall on the contrary Side of the Ordinate, in refpecT: of the Vertex or beginning of theAbfcifTe; as in the Hyperbola, and Hyperboliform Figures.
And, univerfally, in all Paraboliform, and Hyperboliform Figures, the Sub-tangent is equal to the Exponent of the Power of the Ordinate, multiplied into the Abfcifs. Thus in the common Parabola, whofe Property \sfx=yy. The Subtangent is in Length, equal to x, the Abfcifs multi- plied by 2, the Exponent of the Power of y y, the Square of the Ordinate; that is, it is equal to twice the Abfcifs ; and by the former Rule for Paraboliform Figures, it mull be taken above the Ordinate, in the Axis produced.
Thus, alfo, in one of the cubical Paraboloids, where $xx=yyy. The Length of the Sub-tangent will be \ of the Abfcifs. Thus in the Figure, you will fe* that the Sub- tangent in any Curve is a Line, which determines the Inter- section of the Tangent in the Axis.
SUBTENSE, in Geometry, a right Line, oppofite to an Angle, and prcfumed to be drawn between the two Ex- tremities of the Arch, which mcafures that Angle. See Arch.
The Subtenfe of the Angle coincides with the Chord of the Arch. See Chord.
In every reftangleTriangle, the Square of the £&&££«£ of the right Angle, is equal to the Squares of the Subtenfes of both the other Angles ; by the 47th 'Prop, of Euclid. This wonderful Property of that Triangle, was firit difcover'd by Pythagoras, who in the Tranfport of Joy, hereby occafion'd, facrificed a Hecatomb. See Triangle.
The Word is form'd from the Latin, fub, under, and tendo, I ftretch.
SUBTERRANEOUS, fomething under Ground. See Fossil.
Naturalifls talk much of Subterranean Fires, as the Caufe of Volcano's. See Fire and Volcano.
Subterranean Winds, as the Caufe of Earthquakes. See Earthquake.
Mr. Boyle gives us an Inftance, from the Differtation de Admirand. Hangar. Aquh > of a huge Subterraneous Oak
dug out of a Salt Mine in 7ranfylvam'a t fo hard, that if could not eaiily be wrought on by Iron Tools ; which vet being expofed to the Air out of the Mine, became ft rotten* that in four Days, it was eafy to be broken and crumbled between one's Fingers.
Mr. Tterham adds, That the Trees turned out of the Earth, by the Breaches at Weft iJhurrock and %)agenham though probably no other than Alder, and interred mam? Ages ago, in a rotten, oozy Mould, were fo exceedingly tough, hard and found at firft, that he could make but little Impreflions on them with the Strokes of an Ax; yet being expofed to the Air and Water, foon became fo rotten, as to be crumbled between the Fingers.
SUBTILE,inPhyficks, intimates aThing exceedingly fmall fine, and delicate ; fuch as the Animal Spirits, &c. the Effluvia of odorous Bodies, &c. are fuppofed to be. See Efi-'luv^
One kind of Matter is only more fubtile than another, in that being divided into fmaller Parts, and thofe, too, more agitated ; on the one hand, it makes lefs Refiftance to othec Bodies ; and on the other, inimuates itfelf more eaiily into their Pores.
The Cartefians fuppofe a fubtile Matter for their firfl Efe. ment. See Cartesianism and Element.
This they lay down as fo exceedingly Fine, that it penetrates the minute Pores of Glafs and other folid Bodies ; and from this they account for moll of the Phenomena of Nature, See Vacuum, Plenum, Suction, &c.
Yet they don't pretend to prove the Exiftence of this Matter, otherwife than by Confequence. See Materia Subtilis.
Subtile Matter. See Matter.
SUBTILIZATION, the Aft of fubtilizhg, or rendering anything fmaller and fubtiler z, particularly, the diffolving or changing a mixt Body into a pure Liquor, or a fine Powder.
SUBTRIPLE Ratio., is when one Number or Quantity is contain'd in another three times ; thus 2 is faid to be Sub- triple of 6, as 6 is Triple, of 2. See Ratio.
SUBURBICARY, an Epithet given to thofe Provinces of Italy, &c, which compoied the ancient Diocefe or Patri- archate of Rome. See Province.
The Term is form'd from the Latin, fub, under, and urbs. City. They were alio fbmetimes call'd Urbicary Provinces.
Authors ufually reckon Ten of thefe Suburbicary Provinces ; whereof Italy t from the 'Po to the Heel made Seven, and the Iiles of Sicily, Sardinia, and Corfica, the other Three.
Xet Salmafkis will have the Suburbicary Provinces confined to thoie Four in the Neighbourhood of Rome, to which the Authority of the Prefect of Rome extended ; and thefe he makes the Limits of the Diocefe of ancient Rome. See Diocese.
F. Sirmond takes the other Extreme, and comprehends all the Weft under the Name of Suburbicary Provinces. Rufinus, who lived in the Age of the Council of Nice, explains the Power afcribed to the Pope, in the Sixth Canon of that Council, by faying, That he had the Care and Intendance of the Suburbicary Provinces. Hence, the different Sentirnents of Authors , with regard to the Suburbicary Provinces ; fome only confidering the Pope as BiJhop of Rome 5 others, as Patriarch of the Weft, $$c.
SUCCEDANEUM, in Pharmacy, a Remedy fubflituted in the Place of another firfl prefcribed, when the Ingredients are wanting, neceflary for the Compofition of that other. See Substitute.
Substitute and Succedanemn, are of equal Import, unlefs, with fome Authors, we chufe to ufe Substitute, where a Simple of like Virtue is put for another ; and Succedaneu& y where a Compound is ufed with the fame Intention.
The Word is form'd from the Latin, Succedo, to fucceed, to come after.
SUCCENTURIAT_£, in Anatomy. See Renes Sue- centuriatte.
SUCCENTURIATION, the Aft of Subflituting. See Substitution.
SUCCENTURIATUS, in Anatomy, a Mufcle, call'd alfo tpyramidalis. See Pyramidalis.
SUCCESSION, in Philofophy, an Idea we get, by re- flecting on that Train of Ideas conflantly following one an- other in our Minds when awake. See Idea and Mode.
The Diftance between any Parts of this SucceJJion, is what we call Miration. When this SucceJJion of Ideas ceafes, we have no Perception of Time or Duration thereof; but the Moment we fall afleep, and that wherein we awake, feem connecled. See Dur ation.
They, who think we get the Idea of Succeffion from our Obfervarion of Motion "by our Senfes, will come into Mr. Lock's Sentiment, above, when they confider that Motion produces an Idea of Succeffion no otherwife, than by pro- ducing a continued Train of diftinguifhable Ideas. _
A Man that looks on a Body moving, perceives no Motion, unlefs that Motion produce a conflant Train of fucceffive Ideas. But where-ever a Man is, though all Things be
