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Chilo mycterus geometricus

Bur fish Bur" fish` (Zo["o]l.) A spinose, plectognath fish of the Allantic coast of the United States (esp. Chilo mycterus geometricus) having the power of distending its body with water or air, so as to resemble a chestnut bur; -- called also ball fish, balloon fish, and swellfish.

Bur fish Bur" fish` (Zo["o]l.) A spinose, plectognath fish of the Allantic coast of the United States (esp. Chilo mycterus geometricus) having the power of distending its body with water or air, so as to resemble a chestnut bur; -- called also ball fish, balloon fish, and swellfish.

Geometric lathe

3. The movable swing frame of a loom, carrying the reed for separating the warp threads and beating up the weft; -- called also lay and batten. Blanchard lathe, a lathe for turning irregular forms after a given pattern, as lasts, gunstocks, and the like. Drill lathe, or Speed lathe, a small lathe which, from its high speed, is adapted for drilling; a hand lathe. Engine lathe, a turning lathe in which the cutting tool has an automatic feed; -- used chiefly for turning and boring metals, cutting screws, etc. Foot lathe, a lathe which is driven by a treadle worked by the foot. Geometric lathe. See under Geometric Hand lathe, a lathe operated by hand; a power turning lathe without an automatic feed for the tool. Slide lathe, an engine lathe. Throw lathe, a small lathe worked by one hand, while the cutting tool is held in the other.

3. The movable swing frame of a loom, carrying the reed for separating the warp threads and beating up the weft; -- called also lay and batten. Blanchard lathe, a lathe for turning irregular forms after a given pattern, as lasts, gunstocks, and the like. Drill lathe, or Speed lathe, a small lathe which, from its high speed, is adapted for drilling; a hand lathe. Engine lathe, a turning lathe in which the cutting tool has an automatic feed; -- used chiefly for turning and boring metals, cutting screws, etc. Foot lathe, a lathe which is driven by a treadle worked by the foot. Geometric lathe. See under Geometric Hand lathe, a lathe operated by hand; a power turning lathe without an automatic feed for the tool. Slide lathe, an engine lathe. Throw lathe, a small lathe worked by one hand, while the cutting tool is held in the other.

Geometric pen

Bow pen. See Bow-pen. Dotting pen, a pen for drawing dotted lines. Drawing, or Ruling, pen, a pen for ruling lines having a pair of blades between which the ink is contained. Fountain pen, Geometric pen. See under Fountain, and Geometric. Music pen, a pen having five points for drawing the five lines of the staff. Pen and ink, or pen-and-ink, executed or done with a pen and ink; as, a pen and ink sketch. Pen feather. A pin feather. [Obs.] Pen name. See under Name. Sea pen (Zo["o]l.), a pennatula. [Usually written sea-pen.]

Bow pen. See Bow-pen. Dotting pen, a pen for drawing dotted lines. Drawing, or Ruling, pen, a pen for ruling lines having a pair of blades between which the ink is contained. Fountain pen, Geometric pen. See under Fountain, and Geometric. Music pen, a pen having five points for drawing the five lines of the staff. Pen and ink, or pen-and-ink, executed or done with a pen and ink; as, a pen and ink sketch. Pen feather. A pin feather. [Obs.] Pen name. See under Name. Sea pen (Zo["o]l.), a pennatula. [Usually written sea-pen.]

Geometrical pace

Pace Pace, n. [OE. pas, F. pas, from L. passus a step, pace, orig., a stretching out of the feet in walking; cf. pandere, passum, to spread, stretch; perh. akin to E. patent. Cf. Pas, Pass.] 1. A single movement from one foot to the other in walking; a step. 2. The length of a step in walking or marching, reckoned from the heel of one foot to the heel of the other; -- used as a unit in measuring distances; as, he advanced fifty paces. ``The heigh of sixty pace .' --Chaucer. Note: Ordinarily the pace is estimated at two and one half linear feet; but in measuring distances be stepping, the pace is extended to three feet (one yard) or to three and three tenths feet (one fifth of a rod). The regulation marching pace in the English and United States armies is thirty inches for quick time, and thirty-six inches for double time. The Roman pace (passus) was from the heel of one foot to the heel of the same foot when it next touched the ground, five Roman feet. 3. Manner of stepping or moving; gait; walk; as, the walk, trot, canter, gallop, and amble are paces of the horse; a swaggering pace; a quick pace. --Chaucer. To-morrow, and to-morrow, and to-morrow, Creeps in this petty pace from day to day. --Shak. In the military schools of riding a variety of paces are taught. --Walsh. 4. A slow gait; a footpace. [Obs.] --Chucer. 5. Specifically, a kind of fast amble; a rack. 6. Any single movement, step, or procedure. [R.] The first pace necessary for his majesty to make is to fall into confidence with Spain. --Sir W. Temple. 7. (Arch.) A broad step or platform; any part of a floor slightly raised above the rest, as around an altar, or at the upper end of a hall. 8. (Weaving) A device in a loom, to maintain tension on the warp in pacing the web. Geometrical pace, the space from heel to heel between the spot where one foot is set down and that where the same foot is again set down, loosely estimated at five feet, or by some at four feet and two fifths. See Roman pace in the Note under def. 2. [Obs.] To keep, or hold, pace with, to keep up with; to go as fast as. ``In intellect and attainments he kept pace with his age.' --Southey.

Pace Pace, n. [OE. pas, F. pas, from L. passus a step, pace, orig., a stretching out of the feet in walking; cf. pandere, passum, to spread, stretch; perh. akin to E. patent. Cf. Pas, Pass.] 1. A single movement from one foot to the other in walking; a step. 2. The length of a step in walking or marching, reckoned from the heel of one foot to the heel of the other; -- used as a unit in measuring distances; as, he advanced fifty paces. ``The heigh of sixty pace .' --Chaucer. Note: Ordinarily the pace is estimated at two and one half linear feet; but in measuring distances be stepping, the pace is extended to three feet (one yard) or to three and three tenths feet (one fifth of a rod). The regulation marching pace in the English and United States armies is thirty inches for quick time, and thirty-six inches for double time. The Roman pace (passus) was from the heel of one foot to the heel of the same foot when it next touched the ground, five Roman feet. 3. Manner of stepping or moving; gait; walk; as, the walk, trot, canter, gallop, and amble are paces of the horse; a swaggering pace; a quick pace. --Chaucer. To-morrow, and to-morrow, and to-morrow, Creeps in this petty pace from day to day. --Shak. In the military schools of riding a variety of paces are taught. --Walsh. 4. A slow gait; a footpace. [Obs.] --Chucer. 5. Specifically, a kind of fast amble; a rack. 6. Any single movement, step, or procedure. [R.] The first pace necessary for his majesty to make is to fall into confidence with Spain. --Sir W. Temple. 7. (Arch.) A broad step or platform; any part of a floor slightly raised above the rest, as around an altar, or at the upper end of a hall. 8. (Weaving) A device in a loom, to maintain tension on the warp in pacing the web. Geometrical pace, the space from heel to heel between the spot where one foot is set down and that where the same foot is again set down, loosely estimated at five feet, or by some at four feet and two fifths. See Roman pace in the Note under def. 2. [Obs.] To keep, or hold, pace with, to keep up with; to go as fast as. ``In intellect and attainments he kept pace with his age.' --Southey.

Geometrical progression

Progression Pro*gres"sion, n. [L. progressio: cf. F. progression.] 1. The act of moving forward; a proceeding in a course; motion onward. 2. Course; passage; lapse or process of time. I hope, in a short progression, you will be wholly immerged in the delices and joys of religion. --Evelyn. 3. (Math.) Regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical, geometrical, or harmonic. 4. (Mus.) A regular succession of tones or chords; the movement of the parts in harmony; the order of the modulations in a piece from key to key. Arithmetical progression, a progression in which the terms increase or decrease by equal differences, as the numbers [lbrace2]2, 4, 6, 8, 1010, 8, 6, 4, 2[rbrace2] by the difference 2. Geometrical progression, a progression in which the terms increase or decrease by equal ratios, as the numbers [lbrace2]2, 4, 8, 16, 32, 6464, 32, 16, 8, 4, 2[rbrace2] by a continual multiplication or division by 2. Harmonic progression, a progression in which the terms are the reciprocals of quantities in arithmetical progression, as 1/2, 1/4, 1/6, 1/8, 1/10.

Progression Pro*gres"sion, n. [L. progressio: cf. F. progression.] 1. The act of moving forward; a proceeding in a course; motion onward. 2. Course; passage; lapse or process of time. I hope, in a short progression, you will be wholly immerged in the delices and joys of religion. --Evelyn. 3. (Math.) Regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical, geometrical, or harmonic. 4. (Mus.) A regular succession of tones or chords; the movement of the parts in harmony; the order of the modulations in a piece from key to key. Arithmetical progression, a progression in which the terms increase or decrease by equal differences, as the numbers [lbrace2]2, 4, 6, 8, 1010, 8, 6, 4, 2[rbrace2] by the difference 2. Geometrical progression, a progression in which the terms increase or decrease by equal ratios, as the numbers [lbrace2]2, 4, 8, 16, 32, 6464, 32, 16, 8, 4, 2[rbrace2] by a continual multiplication or division by 2. Harmonic progression, a progression in which the terms are the reciprocals of quantities in arithmetical progression, as 1/2, 1/4, 1/6, 1/8, 1/10.

geometrical proportion

Proportion Pro*por"tion, n. [F., fr. L. proportio; pro before + portio part or share. See Portion.] 1. The relation or adaptation of one portion to another, or to the whole, as respect magnitude, quantity, or degree; comparative relation; ratio; as, the proportion of the parts of a building, or of the body. The image of Christ, made after his own proportion. --Ridley. Formed in the best proportions of her sex. --Sir W. Scott. Documents are authentic and facts are true precisely in proportion to the support which they afford to his theory. --Macaulay. 2. Harmonic relation between parts, or between different things of the same kind; symmetrical arrangement or adjustment; symmetry; as, to be out of proportion. ``Let us prophesy according to the proportion of faith.' --Rom. xii. 6. 3. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot. Let the women . . . do the same things in their proportions and capacities. --Jer. Taylor. 4. A part considered comparatively; a share. 5. (Math.) (a) The equality or similarity of ratios, especially of geometrical ratios; or a relation among quantities such that the quotient of the first divided by the second is equal to that of the third divided by the fourth; -- called also geometrical proportion, in distinction from arithmetical proportion, or that in which the difference of the first and second is equal to the difference of the third and fourth. Note: Proportion in the mathematical sense differs from ratio. Ratio is the relation of two quantities of the same kind, as the ratio of 5 to 10, or the ratio of 8 to 16. Proportion is the sameness or likeness of two such relations. Thus, 5 to 10 as 8 to 16; that is, 5 bears the same relation to 10 as 8 does to 16. Hence, such numbers are said to be in proportion. Proportion is expressed by symbols thus: a:b::c:d, or a:b = c:d, or a/b = c/d. (b) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional. Continued proportion, Inverse proportion, etc. See under Continued, Inverse, etc. Harmonical, or Musical, proportion, a relation of three or four quantities, such that the first is to the last as the difference between the first two is to the difference between the last two; thus, 2, 3, 6, are in harmonical proportion; for 2 is to 6 as 1 to 3. Thus, 24, 16, 12, 9, are harmonical, for 24:9::8:3. In proportion, according as; to the degree that. ``In proportion as they are metaphysically true, they are morally and politically false.' --Burke.

Proportion Pro*por"tion, n. [F., fr. L. proportio; pro before + portio part or share. See Portion.] 1. The relation or adaptation of one portion to another, or to the whole, as respect magnitude, quantity, or degree; comparative relation; ratio; as, the proportion of the parts of a building, or of the body. The image of Christ, made after his own proportion. --Ridley. Formed in the best proportions of her sex. --Sir W. Scott. Documents are authentic and facts are true precisely in proportion to the support which they afford to his theory. --Macaulay. 2. Harmonic relation between parts, or between different things of the same kind; symmetrical arrangement or adjustment; symmetry; as, to be out of proportion. ``Let us prophesy according to the proportion of faith.' --Rom. xii. 6. 3. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot. Let the women . . . do the same things in their proportions and capacities. --Jer. Taylor. 4. A part considered comparatively; a share. 5. (Math.) (a) The equality or similarity of ratios, especially of geometrical ratios; or a relation among quantities such that the quotient of the first divided by the second is equal to that of the third divided by the fourth; -- called also geometrical proportion, in distinction from arithmetical proportion, or that in which the difference of the first and second is equal to the difference of the third and fourth. Note: Proportion in the mathematical sense differs from ratio. Ratio is the relation of two quantities of the same kind, as the ratio of 5 to 10, or the ratio of 8 to 16. Proportion is the sameness or likeness of two such relations. Thus, 5 to 10 as 8 to 16; that is, 5 bears the same relation to 10 as 8 does to 16. Hence, such numbers are said to be in proportion. Proportion is expressed by symbols thus: a:b::c:d, or a:b = c:d, or a/b = c/d. (b) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional. Continued proportion, Inverse proportion, etc. See under Continued, Inverse, etc. Harmonical, or Musical, proportion, a relation of three or four quantities, such that the first is to the last as the difference between the first two is to the difference between the last two; thus, 2, 3, 6, are in harmonical proportion; for 2 is to 6 as 1 to 3. Thus, 24, 16, 12, 9, are harmonical, for 24:9::8:3. In proportion, according as; to the degree that. ``In proportion as they are metaphysically true, they are morally and politically false.' --Burke.

geometrical square

Quadrat Quad"rat, n. [F. quadrat, cadrat. See Quadrate.] 1. (Print.) A block of type metal lower than the letters, -- used in spacing and in blank lines. [Abbrev. quad.] 2. An old instrument used for taking altitudes; -- called also geometrical square, and line of shadows.

Quadrat Quad"rat, n. [F. quadrat, cadrat. See Quadrate.] 1. (Print.) A block of type metal lower than the letters, -- used in spacing and in blank lines. [Abbrev. quad.] 2. An old instrument used for taking altitudes; -- called also geometrical square, and line of shadows.

Geometrically

Geometrically Ge`o*met"ric*al*ly, adv. According to the rules or laws of geometry.

Geometrically Ge`o*met"ric*al*ly, adv. According to the rules or laws of geometry.

Geometrician

Geometrician Ge*om`e*tri"cian, n. One skilled in geometry; a geometer; a mathematician.

Geometrician Ge*om`e*tri"cian, n. One skilled in geometry; a geometer; a mathematician.

Ratio of a geometrical progression

Ratio Ra"ti*o, n. [L., fr. reri, ratus, to reckon, believe, think, judge. See Reason.] 1. (Math.) The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b by a/b; or (less commonly) the second is made the dividend; as, a:b = b/a. Note: Some writers consider ratio as the quotient itself, making ratio equivalent to a number. The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule. 2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress. Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc. Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.

Ratio Ra"ti*o, n. [L., fr. reri, ratus, to reckon, believe, think, judge. See Reason.] 1. (Math.) The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b by a/b; or (less commonly) the second is made the dividend; as, a:b = b/a. Note: Some writers consider ratio as the quotient itself, making ratio equivalent to a number. The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule. 2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress. Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc. Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.

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