Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	join_v	line_n	rational_a	2,576	5	12.5481	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A05115	Via regia ad geometriam. = The vvay to geometry Being necessary and usefull, for astronomers. Geographers. Land-meaters. Sea-men. Engineres. Architecks. Carpenters. Paynters. Carvers, &c. Written in Latine by Peter Ramus, and now translated and much enlarged by the learned Mr. William Bedvvell.; Via regia ad geometriam. English	Ramus, Petrus, 1515-1572.; Bedwell, William, ca. 1561-1632.; Clarke, John, d. 1658.	1636 (1636)	STC 15251; ESTC S108337	93,096	205

greater than the base i u. Therefore by the 5 e vij the angle o e i is greater than the angle i e u. Therefore two angles a e o and o e i are greater than a e i. 10 A plaine solid is a Pyramis or a Pyramidate 11 A Pyramis is a plaine solid from a rectilineall base equally decreasing As here thou conceivest from the triangular base a e i unto the toppe o the triangles a o e a o i and e o i to be reared up Therefore 12 The sides of a pyramis are one more than are the base The sides are here named Hedrae And 13 A pyramis is the first figure of solids For a pyramis in solids is as a triangle is in plaines For a pyramis may be resolved into other solid figures but it cannot be resolved into any one more simple than it selfe and which consists of fewer sides than it doth Therefore 14 Pyramides of equall heighth are as their bases are 5 e and 6. p xij And 15 Those which are reciprocall in base and heighth are equall 9 p xij These consectaries are drawne out of the 16 18 e. iiij 16 A tetraedrum is an ordinate pyramis comprehended of foure triangles 26. d xj Therefore 17 The edges of a tetraedrum are sixe the plaine angles twelve the solide angles foure For a Tetraedrum is comprehended of foure triangles each of them having three sides and three corners a peece And every side is twise taken Therefore the number of edges is but halfe so many And 18 Twelve tetraedra's doe fill up a solid place Because 8. solid right angles filling a place and 12. angles of the tetraedrum are equall betweene themselves seeing that both of them are comprehended of 24. plaine right-angles For a solid right angle is comprehended of three plaine right angles And therefore 8. are comprehended of 24. In like manner the angle of a Tetraedrum is comprehended of three plaine equilaters that is of sixe third of one right angle and therefore of two right angles Therefore 12 are comprehended of 24. And 19 If foure ordinate and equall triangles be joyned together in solid angles they shall comprehend a tetraedrum 20. If a right line whose power is sesquialter unto the side of an equilater triangle be cut after a double reason the double segment perpendicular to the center of the triangle knit together with the angles thereof shall comprehend a tetraedrum 13 p xiij For a solid to be comprehended of right lines understand plaines comprehended of right lines as in other places following The twenty third Booke of Geometry of a Prisma 1 A Pyramidate is a plaine solid comprehended of pyramides 2. A pyramidate is a Prisma or a mingled polyedrum 3. A prisma is a pyramidate whose opposite plaines are equall alike and parallell the rest parallelogramme 13 dxj. Therefore 4. The flattes of a prisma are two more than are the angles in the base And indeed as the augmentation of a Pyramis from a quaternary is infinite so is it of a Prisma from a quinary As if it be from a triangular quadrangular or quinquangular base you shal have a Pentaedrum Hexaedrum Heptaedrum and so in infinite 5. The plaine of the base and heighth is the solidity of a right prisma 6. A prisma is the triple of a pyramis of equall base and heighth è 7 p. x i j. If the base be triangular the Prisma may be resolved into prisma's of triangular bases and the theoreme shall be concluded as afore Therefore 7. The plaine made of the base and the third part of the heighth is the solidity of a pyramis of equall base and heighth So in the example following Let 36 the quadrate of 6 the ray be taken out of 292 9 1156 the quadrate of the side 17 3 34 the side 16 3 34 of 256 9 1156 the remainder shall be the height whose third part is 5 37 102 the plaine of which by the base 72 ¼ shall be 387 11 24 for the solidity of the pyramis given After this manner you may measure an imperfect Prisma 8. Homogeneall Prisma's of equall heighth are one to another as their bases are one to another 29 30,31 32 p xj This element is a consectary out of the 16 e iiij And 9. If they be reciprocall in base and heighth they are equall This is a Consectary out the 18 e iiij And 10. If a Prisma be cut by a plaine parallell to his opposite flattes the segments are as the bases are 25 p. xj 11. A Prisma is either a Pentaedrum or Compounded of pentaedra's Here the resolution sheweth the composition 12 If of two pentaedra's the one of a triangular base the other of a parallelogramme base double unto the triangular be of equall heighth they are equall 40. p xj The canse is manifest and briefe Because they be the halfes of the same prisma As here thou maist perccive in a prisma cut into two halfes by the diagoni's of the opposite sides Euclide doth demonstrate it thus Let the Pentaedra's a e i o u and y s r l m be of equall heighth the first of a triangular base e i o The second of a parallelogramme base s l double unto the triangular Now let both of them be double and made up so that first be n● The second y s r l v f. Now againe by the grant the base s l is the double of the base e i o whose double is th● base e o by the 12 e x. Therefore the bases s l and e o are equall And therefore seeing the prisma's by the grant here are of equall heighth as the bases by the conclusion are equall the prisma's are equall And therefore also their halfes a e i o u and y s n l r are equall The measuring of a pentaedrall prisma was even now generally taught The matter in speciall may be conceived in these two examples following The plaine of 18. the perimeter of the triangular base and 12 the heighth is 216. This added to the triangular base 15 18 3● or 15 ⅗ almost twise taken that is 31 ⅕ doth make 247 ⅕ for the summe of the whole surface But the plaine of the same base 15 ⅖ and the heighth 12. is 187 ⅕ for the whole solidity So in the pentaedrum the second prisma which is called Cuneus a wedge of the sharpnesse and which also more properly of cutting is called a prisma the whole surface is 150 and the solidity 90. 13 A prisma compounded of penta●dra's is either an Hexaedrum or Polyedrum And the Hexaedrum is either a Parallelepipedum or a Trapezium 14 A parallelepipedum is that whose opposite plaines are parallelogrammes ê 24. p xj Therefore a Parallelepipedum in solids answereth to a Parallelogramme in plaines For here the opposite Hedrae or flattes are parallell There the opposite sides are parallell Therefore 15 It is cut into two halfes with a plaine by the diagonies of the opposite

quem Agricola alijex antiquis monumentis tradi derunt Now by any one of these knowne and compared with ours to all English men well knowne the rest may easily be proportioned out 2. The thing proposed to bee measured is a Magnitude Magnitudo a Magnitude or Bignesse is the subject about which Geometry is busied For every Art hath a proper subject about which it doth employ al his rules and precepts And by this especially they doe differ one from another So the subject of Grammar was speech of Logicke reason of Arithmeticke numbers and so now of Geometry it is a magnitude all whose kindes differences and affections are hereafter to be declared 3. A Magnitude is a continuall quantity A Magnitude is quantitas continua a continued or continuall quantity A number is quantitas discreta a disjoined quantity As one two three foure doe consist of one two three foure unities which are disjoyned and severed parts whereas the parts of a Line Surface and Body are contained and continued without any manner of disjunction separation or distinction at all as by and by shall better and more plainely appeare Therefore a Magnitude is here understood to be that whereby every thing to be measured is said to bee great As a Line from hence is said to be long a Surface broade a Body solid Wherefore Length Breadth and solidity are Magnitudes 4. That is continuum continuall whose parts are contained or held together by some common bound This definition of it selfe is somewhat obscure and to be understand onely in a geometricall sense And it dependeth especially of the common bounde For the parts which here are so called are nothing in the whole but in a potentia or powre Neither indeede may the whole magnitude bee conceived but as it is compact of his parts which notwithstanding wee may in all places assume or take as conteined and continued with a common bound which Aristotle nameth a Common limit but Euclide a Common section as in a line is a Point in a surface a Line in a body a Surface 5. A bound is the outmost of a Magnitude Terminus a Terme or Bound is here understood to bee that which doth either bound limite or end actu in deede as in the beginning and end of a magnitude Or potentia in powre or ability as when it is the common bound of the continuall magnitude Neither is the Bound a parte of the bounded magnitude For the thing bounding is one thing and the thing bounded is another For the Bound is one distance dimension or degree inferiour to the thing bounded A Point is the bound of a line and it is lesse then a line by one degree because it cannot bee divided which a line may A Line is the bound of a surface and it is also lesse then a surface by one distance or dimension because it is only length wheras a surface hath both length and breadth A Surface is the bound of a body and it is lesse likewise then it is by one dimension because it is onely length and breadth whereas as a body hath both length breadth and thickenesse Now every Magnitude actu in deede is terminate bounded and finite yet the geometer doth desire some time to have an infinite line granted him but no otherwise infinite or farther to bee drawane out then may serve his turne 6. A Magnitude is both infinitely made and continued and cut or divided by those things wherewith it is bounded A line a surface and a body are made gemetrically by the motion of a point line and surface Item they are conteined continued and cut or divided by a point line and surface But a Line is bounded by a point a surface by a line And a Body by a surface as afterward by their severall kindes shall be understood Now that all magnitudes are cut or divided by the same wherewith they are bounded is conceived out of the definition of Continuum e. 4. For if the common band to containe and couple together the parts of a Line surface Body be a Point Line and Surface it must needes bee that a section or division shall be made by those common bandes And that to bee dissolved which they did containe and knitt together 7. A point is an undivisible signe in a magnitude A Point as here it is defined is not naturall and to bee perceived by sense Because sense onely perceiveth that which is a body And if there be any thing lesse then other to be perceived by sense that is called a Point Wherefore a Point is no Magnitude But it is onely that which in a Magnitude is conceived and imagined to bee undivisible And although it be voide of all bignesse or Magnitude yet is it the beginning of all magnitudes the beginning I meane potentiâ in powre 8. Magnitudes commensurable are those which one and the same measure doth measure contrariwise Magnitudes incommensurable are those which the same measure cannot measure 1 2. d. X. Magnitudes compared betweene themselves in respect of numbers have Symmetry or commensurability and Reason or rationality Of themselves Congruity and Adscription But the measure of a magnitude is onely by supposition and at the discretion of the Geometer to take as pleaseth him whether an ynch an hand breadth foote or any other thing whatsoever for a measure Therefore two magnitudes the one a foote long the other two foote long are commensurable because the magnitude of one foote doth measure them both the first once the second twice But some magnitudes there are which have no common measure as the Diagony of a quadrate and his side 116. p. X. actu in deede are Asymmetra incommensurable And yet they are potentiâ by power symmetra commensurable to witt by their quadrates For the quadrate of the diagony is double to the quadrate of the side 9. Rationall Magnitudes are those whose reason may bee expressed by a number of the measure given Contrariwise they are irrationalls 5. d. X. Ratio Reason Rate or Rationality what it is our Authour and likewise Salignacus have taught us in the first Chapter of the second booke of their Arithmetickes Thither therefore I referre thee Data mensura a Measure given or assigned is of Euclide called Rhetè that is spoken or which may be uttered definite certaine to witt which may bee expressed by some number which is no other then that which as we said was called mensura famosa a knowne or famous measure Therefore Irrationall magnitudes on the contrary are understood to be such whose reason or rate may not bee expressed by a number or a measure assigned As the side of the side of a quadrate of 20. foote unto a magnitude of two foote of which kinde of magnitudes thirteene sorts are mentioned in the tenth booke of Euclides Elements such are the segments of a right line proportionally cutte unto the whole line The Diameter in a circle is rationall But it is irrationall unto the side of