What is a line in mathematics. How are lines defined in geometry. What are the different types of lines. Can you provide real-world examples of lines. What is the history behind the concept of lines. How do lines relate to other geometric concepts.
The Fundamental Concept of Lines in Mathematics
In the realm of geometry, a line stands as a foundational concept. But what exactly is a line? A line is defined as a straight, one-dimensional figure that extends infinitely in both directions without any thickness. This abstract mathematical entity plays a crucial role in various geometric principles and real-world applications.
Key characteristics of a line include:
- It has no endpoints
- It extends infinitely in both directions
- It has no width or thickness
- It is composed of an infinite number of points
Is there a way to measure the length of a line? Due to its infinite nature, a line cannot be measured. However, we can measure portions of a line, which brings us to the concept of line segments.
Line Segments: A Measurable Portion of a Line
While a line itself is infinite, a line segment represents a finite portion of a line with two defined endpoints. Unlike a line, a line segment can be measured, with its length determined by the distance between its two endpoints.
How does a line segment differ from a line?
- A line segment has two defined endpoints
- It has a measurable length
- It is a part of a line, not infinite in extent
Types of Lines: Exploring Geometric Variations
Lines come in various forms, each with unique properties and applications in geometry and real-world scenarios. Understanding these types enhances our grasp of spatial relationships and geometric principles.
Straight Lines: The Classic Definition
A straight line is the most basic and commonly recognized type of line. It consists of a set of collinear points extending infinitely in opposite directions without any curves.
Curved Lines: Bending the Rules
Contrary to straight lines, curved lines exhibit a bend or curvature in their formation. They still consist of collinear points but follow a non-linear path.
Oblique Lines: The Diagonal Approach
An oblique line is neither horizontal, vertical, nor parallel to any reference line. It presents a slanting or diagonal appearance.
Horizontal and Vertical Lines: Defining Spatial Orientation
Horizontal lines run parallel to the horizon, extending from left to right or vice versa. Vertical lines, on the other hand, run perpendicular to horizontal lines, extending from top to bottom or bottom to top.
Line Relationships: When Lines Interact
The interaction between lines gives rise to various geometric concepts and relationships. These interactions form the basis for more complex geometric principles and real-world applications.
Parallel Lines: Never-Meeting Companions
Parallel lines are two or more lines on the same plane that maintain a constant distance between them and never intersect, no matter how far they are extended.
Intersecting Lines: Points of Convergence
When two or more lines on the same plane cross each other at a specific point, they are called intersecting lines. The point where they meet is known as the point of intersection.
Transversal Lines: Crossing Paths
A transversal line is one that passes through two or more parallel or non-parallel lines. This concept is crucial in understanding angles formed by intersecting lines.
Perpendicular Lines: The Right Angle Relation
Perpendicular lines are two lines that intersect at a 90-degree angle. This relationship is fundamental in many geometric calculations and real-world applications.
Real-World Applications of Lines
Lines are not just abstract mathematical concepts; they surround us in our daily lives. Recognizing these real-world representations can help us better understand and appreciate the concept of lines.
Where can we find examples of lines in our everyday environment?
- The edge of a ruler or a pencil represents a straight line
- The horizon where the sky meets the earth forms a horizontal line
- The sides of a building often showcase vertical lines
- Roads and railways often follow straight or curved lines
- The path of light rays can be represented as straight lines
How do these real-world examples help us understand the concept of lines? By observing these everyday instances, we can grasp the abstract mathematical concept more concretely, making it easier to apply in various fields such as architecture, engineering, and design.
The Historical Context of Lines in Mathematics
The concept of lines has a rich history in mathematics, dating back to ancient civilizations. Understanding this historical context can provide valuable insights into the development of geometric principles.
Euclid’s Contribution to Line Theory
Euclid, often referred to as the “Father of Geometry,” played a pivotal role in formalizing the concept of lines. In his influential work “Elements,” Euclid defined a line as “breadthless length,” laying the foundation for much of the geometric principles we use today.
How did Euclid’s definition influence modern mathematics? His concise yet profound description of a line as having length but no width or thickness continues to shape our understanding of this fundamental geometric concept.
Evolution of Line Concept Through History
The concept of lines has evolved over time, with various mathematicians and cultures contributing to our current understanding. From ancient Egyptian and Babylonian practices to modern-day computational geometry, the idea of lines has been refined and expanded.
What are some key milestones in the development of line theory?
- Ancient Egyptians used lines in construction and land surveying
- Greek mathematicians like Thales and Pythagoras developed theorems involving lines
- René Descartes introduced the Cartesian coordinate system, allowing lines to be represented algebraically
- Modern mathematicians have extended line concepts to non-Euclidean geometries
Lines in Relation to Other Geometric Concepts
Lines do not exist in isolation; they form the basis for many other geometric concepts and shapes. Understanding these relationships enhances our overall grasp of geometry.
Lines and Angles
When two lines intersect, they form angles. The study of these angles and their properties is crucial in trigonometry and many real-world applications.
Lines and Polygons
Polygons are closed shapes formed by connecting line segments. The properties of these line segments determine the characteristics of the polygon.
Lines in Three-Dimensional Space
While we often think of lines in two dimensions, they also play a crucial role in three-dimensional geometry. Lines in 3D space form the edges of solids and are essential in understanding spatial relationships.
Practical Applications of Line Concepts
The understanding of lines extends far beyond mathematical theory. It has practical applications in various fields, influencing how we perceive and interact with the world around us.
Lines in Architecture and Engineering
Architects and engineers rely heavily on line concepts for design and construction. Straight lines often represent structural elements, while curved lines can add aesthetic appeal or serve specific functional purposes.
Lines in Art and Design
Artists and designers use lines as fundamental elements to create form, convey emotion, and guide the viewer’s eye. Different types of lines can evoke different feelings and perceptions.
Lines in Navigation and Cartography
In navigation and map-making, lines play a crucial role. Latitude and longitude lines help define locations on Earth, while other lines represent routes, boundaries, and topographic features.
How do these applications demonstrate the versatility of line concepts? By observing how lines are used across various disciplines, we can appreciate the fundamental nature of this geometric concept and its impact on our daily lives and technological advancements.
What Is a Line in Math? Definition, Types, Examples, Facts
What is a Line?
In geometry, a line is a straight one-dimensional figure that does not have a thickness, and it extends endlessly in both directions.
Diagram A represents a line. It does not have any endpoint. The two arrows at each end signify that the line extends endlessly and is unending in both directions. The length of a line cannot be measured.
Diagram A: Line
l in the above diagram represents a line.
In simple terms, when a set of collinear points are connected in a one-dimensional plane, it is called a line.
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What is a Line Segment?
A line segment, which is part of a line, has two defined endpoints.
Diagram B represents a line segment with two endpoints, A and B. A line segment can be measured, whereas a line cannot. The length of the line segment is the distance between the two endpoints, A and B.
Diagram B: Line Segment
- Let’s draw a line
To draw a line, take a pencil, a ruler, and a book or a piece of paper.
- Place the ruler on the paper and hold it firmly.
- With the help of the pencil, draw a line along the horizontal edge of the ruler.
- Label the line as either l or m.
Come, let’s sing along!
Length of the table at which you dine,
Ray of the sun in the morning that shine,
The straight tubes and pipes in a pipeline,
We can find in them – straight geometry lines!
• Closely-related concepts to line
To better understand the concept of a line, let’s look at the following diagram along with the explanation mentioned below.
• Examples of a Line
Did you know we are surrounded by objects that represent straight lines? They are all around us.
Let’s look at some real-life objects as examples for your reference.
- A pencil or a pen is a representation of a straight line.
- A straight line is drawn on a piece of paper either horizontally or vertically with a pencil.
- The edge of a table represents a straight line.
- A scale or a ruler, a tool to measure length, is a straight line.
• History of Line
Euclid, a Greek mathematician – fondly known as the Father of Geometry – introduced the concept of a line. He defined it as “a breadthless length.”
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Different Types of Line
Now Let’s understand the different types of lines.
- Straight Line
A line is a set of collinear points with no curves and extends limitlessly in opposite directions is called a Straight line.
- Curved Line
A line is a set of collinear points which has a curvature or bend in its formation is called a Curved Line.
- Oblique Line
An oblique is a line that is diagonal or slanting. However, it is not perpendicular, parallel, vertical, or horizontal.
- Horizontal Line
A horizontal line is a straight line that starts from either left to right or right to left. In simple terms, a horizontal line is also known as a sleeping line.
A particular line at which the earth’s surface and the sky appear to meet is called the horizon. Anything parallel to the horizon is known to be horizontal.
- Vertical Line
A vertical line is a straight line that starts from the top to bottom or bottom to top. In simple terms, a vertical line is also known as a standing line.
Moreover, vertical is the opposite of horizontal. Anything that makes a 90-degree angle or a right angle with the horizontal line or the horizon is called vertical.
Moreover, there are also certain variations of the types of lines.
It occurs when more than one line is placed in the same dimension.
- Parallel Line
A pair of two lines that are on the same plane and the distance between them is equal and remains constant. When such two lines do not intersect with each other, they are known as parallel lines.
- Intersecting Line
On the contrary, when two or more pairs of lines are on the same plane and intersect each other at one given point, they are known as intersecting lines.
- Transversal Line
A transversal line is a line that passes through two or more parallel or non-parallel lines at a given point. The parallel lines and the transversal line must be on the same plane.
- Perpendicular Line
When two lines on the same plane intersect each other and form a 90° angle at the point of intersection, they are known to be perpendicular lines.
• Fun Facts About Lines
Let’s get to know a few interesting facts about lines.
- A line is made up of an infinite number of points.
- A line does not have width or thickness. It can only extend in length limitlessly.
- When we place two points at each end of the line, it forms a line segment. Additionally, when we put one point at one end and an arrow at the other end, it forms a ray.
- If three or more points are placed on the same line, they are called collinear points.
- Euclid, in his book Elements, which is one of the most influential books ever written, has referred to the term line several times.
Solved Examples On Line
- Which of the following diagrams is a line?
Answer: The second diagram is a line as the two endpoints represent and includes an arrow, which extends endlessly in opposite directions.
- Identify the diagram and explain if it is a pair of parallel lines or perpendicular lines?
Answer: The above diagram shows perpendicular lines as both the lines intersect at one point and form an angle of 90° at the intersection.
- Which of the following diagrams shows a pair of parallel lines?
Answer: The 2nd diagram shows a pair of parallel lines, as both are on the same dimensional plane and do not intersect each other.
Practice Problems On Line
1
Choose the correct pair of parallel lines from the given options:
PS II PQ
PS II QR
PQ II SR
QR II SR
Correct answer is: PQ II SR
The correct answer is PQ II SR.
2
Identify the diagram
A line
A ray
A line segment
An angle
Correct answer is: A line
The correct answer is a line as it extends indefinitely in both directions.
3
What type are the below pair of lines known as
Transversal lines
Parallel lines
Horizontal Lines
Intersecting Lines
Correct answer is: Intersecting Lines
The correct answer is intersecting lines, as the lines intersect each other at a point.
Frequently Asked Questions On Line
What is the meaning of a ray?
In geometry, a ray is defined as a one-dimensional figure with a fixed starting point. However, it has no endpoint.
How do you describe a line segment?
A line segment is part of a line that has 2 specified endpoints in both directions and has a definite length.
What is the difference between a line segment and a line?
Unlike a line, which does not have any endpoints, a line segment has two endpoints.
Does a line have width and thickness?
No, a line only has length. It does not have width or thickness.
How many endpoints does a line have?
A line does not have any endpoint. For reference, a ray has one endpoint, and a segment has two endpoints.
How are lines referred to or labeled?
A line can be referred to or labeled using two letters at the ends of the line, usually in uppercase, such as A and B.
A line is generally referred to with a single letter, such as ‘l’ or ‘m’, usually in lowercase.
• Tips to master the concept of Line
We at SplashLearn have curated games, worksheets, and courses for children to identify types of lines and courses to differentiate between lines, line segments, rays, and angles.
It is highly beneficial for children to learn through games and worksheets customized in an interactive and engaging format. It is exciting for them, as their brains tend to grasp visuals more easily and memorize them quickly.
SplashLearn offers personalized grade and standard-based education material. Visit www.splashlearn.com to know more.
line | meaning of line in Longman Dictionary of Contemporary English
From Longman Dictionary of Contemporary EnglishRelated topics: Telephone, telegraph, Trains & railways, Military, Cleaning, Trade, Transport, Drug culturelineline1 /laɪn/ ●●● S1 W1 noun
1 on paper/on the ground [countable]LINE a long thin mark on a piece of paper, the ground, or another surface
Draw a straight line across the top of the page.
Sign your name on the dotted line (=line made up of a series of dots).
The edges of the pitch are marked by white lines.
The goalkeeper just managed to stop the ball going over the line.
He raced towards the finishing line.2 between two areas [countable]LINE an imaginary line on the surface of the Earth, for example showing where one country or area of land stops and another beginscounty/state line American English
He was born in a small town just across the state line.line of latitude/longitude
They were still travelling along the same line of longitude.► see thesaurus at border → International Date Line 3 of people/things [countable] a) LINEa row of people or things next to each otherline of
There was a line of fir trees on either side of the road.
The four men were standing in a line on the other side of the table.
A couple of the posts were out of line (=not in a straight row).
b) LINE especially American English a row of people, cars etc that are waiting one behind the other SYN queue British English
I looked in despair at the long line in front of the ticket office.line of
I joined the line of vehicles waiting to get into the car park.stand/wait in line
Customers stood in line for 20 minutes at the cash register.
He tried to cut in line (=go in front of other people who are waiting).
The woman next in line began to mutter to herself.
4 direction [countable]DIRECTION the direction or imaginary line along which something travels between two places
Light travels in a straight line.
A boat came into my line of vision (=the direction I was looking in).line of fire/attack/movement etc (=the direction in which someone shoots, attacks, moves etc)
I was directly in the animal’s line of attack.
They knew they needed to block their enemy’s supply lines (=the direction used for carrying supplies of food etc).5 on your face [countable]LINE a line on the skin of someone’s face → wrinkle
She frowned, and deep lines appeared between her eyebrows.
There were fine lines around her eyes.
No one can avoid lines and wrinkles as they get older. 6 phone [countable]TCT a telephone wire or connection
I’m sorry, the line is busy (=someone is already using it).
There seems to be a fault on the line.
There was a click, then the line went dead (=suddenly stopped working completely).
Henry is on the line (=on the phone) from New York.
I got on the line to (=phoned) the hospital as soon as I heard about the accident.
I wished he would just get off the line.
I’m sorry, it’s a bad line and I can’t hear you.
Hold the line (=wait on the phone), please, and I’ll put you through to our sales department.
Do you have a separate line for your modem?
7 for trains [countable]TTT a track that a train travels along
We were delayed because of a problem further along the line.
When you get to central London, take the Victoria Line to Finsbury Park.railway line British English, railroad line American English
The trail follows a disused railroad line along the edge of the valley.8 between two types of thing [countable usually singular] the point at which one type of thing can be considered to be something else or at which it becomes a particular thingline between
There is a fine line between superstition and religion.
The dividing line between luxuries and necessities is constantly changing.
Sometimes he found it hard to draw the line between work and pleasure.
Her remarks did not quite cross the line into rudeness.
Large numbers of families are living on or near the poverty line (=the point at which people are considered to be very poor). 9 shape/edge [countable usually plural]SHAPE the outer shape of something long or tall
She was wearing a loose dress which softened the lines of her body.
a modern building with clean, elegant lines.10 words [countable] a) a line of written words, for example in a poem or a document
He quoted a few lines from Shakespeare.
Scroll down to line 29. b) a remark
He liked to introduce himself with a witty opening line.
This was one of his favourite chat-up lines (=remark for impressing someone you want to attract). c) [usually plural] words that someone has to learn and say as part of a play or performance
Paul often messed up his lines.
It always took me ages to learn my lines.
11 opinion/attitudeOPINION [singular] an opinion or attitude, especially one that someone states publicly and that influences their actionsline on
I can’t agree with the government’s line on immigration.
Journalists are often too willing to accept the official line (=the opinion that a government states officially).
He found it hard to accept the party line (=the official opinion of a political party) on every issue.take a tough/firm/hard line on something
The school takes a very tough line on drugs. → toe the line212 way of doing somethingWAY/MANNER [countable] a particular way of doing something or of thinking about somethingline of argument/reasoning/inquiry etc
It seemed useless to pursue this line of questioning.
Opposition parties soon realized they would have to try a different line of attack.
The police are following several different lines of enquiry.
We were both thinking along the same lines (=in the same way).
In South Africa, the press developed along very different lines (=in a very different way).
More groups will now be set up on these lines (=this way).
The company’s rapid success means it’s definitely on the right lines (=doing something the right way).
13 series of events [countable usually singular] a series of events that follow each otherline of
This is the latest in a long line of political scandals.14 in a war [countable]PM the edge of an area that is controlled by an army, where soldiers stay and try to prevent their enemy from moving forward
They finally broke through the German line.
young soldiers who were sent to the front line to fight
One regiment was trapped behind enemy lines.
Reinforcements were available just behind the lines.15 in a company/organization [countable] a series of levels of authority within an organization
Decisions are taken by senior officers and fed down through the line of command to the ordinary soldiers.
There should be more direct discussion between managers and workers lower down the line. → line manager16 of rope/wire [countable]DHC a piece of strong string, rope, or wire used for a particular purpose
She hung the clothes out on the washing line (=line for hanging wet clothes on to dry).
The fishing line (=line for catching fish) snapped and the fish got away.17 product [countable]BBT a type of goods for sale in a shop
The company has just launched a new line of small, low-priced computers.
18 → along these/those lines19 → along religious/ethnic/party etc lines20 → on line21 → drop somebody a line22 → don’t give me that line23 → fall into line/bring somebody into line24 → in line with something25 → bring something into line with something26 → be out of line27 → be in line for something/be in line to do something28 → be first/second/next etc in line to the throne29 → be on the line30 → be in somebody’s line31 → get a line on somebody/something32 → somewhere along the line33 → down the line34 → in the line of duty
35 → be in the firing line/in the line of fire36 → lines37 family [singular]FAMILY your family, considered as the people you are related to who lived before you and the people who will live after you
She comes from a long line of actors.
It looks as if Joe might be the last of the line (=the last in his family).the male/female line
This particular gene is passed down through the male line.line of succession (=the system by which an important position or property is passed from a parent to their children, and then to their children etc)
Henry the Eighth wanted a male heir to ensure the Tudor line of succession.38 job [countable usually singular]JOB/WORK the type of work someone doesline of work/business
What line of business is he in?in the building/retail etc line
She’s keen to do something in the fashion line.39 transport [countable]TT a company that provides transport for moving goods by sea, air, road etc
He runs a transatlantic shipping line.40 drug [countable] informalMDD an amount of an illegal drug in powder form, arranged in a line so it can be breathed in through the nose
→ draw the line at, → draw a line (between something), → where do you draw the line?, → draw a line under something, → hard line, → hook, line and sinker, → lay something on the line, → picket line, → the poverty line/level, → read between the linesTHESAURUSon the ground/on the surface of somethingline a long thin mark on a piece of paper, the ground, or another surfaceThe teacher put a red line through the first sentence.
If the ball goes over the line, it’s out of play.groove a thin line that has been cut into a surfaceDeep grooves had been cut into the stone to channel the water.Lyle ran his fingernail along the groove in the table.rut a deep line in the ground which has been made by the wheels of vehiclesThe deep ruts made by the trucks were full of water.The tractor’s wheels caught a rut in the field and jolted him.crease/wrinkle a line on clothes, material, or paper where it has been folded or crushedShe was trying to smooth out the creases in her dress.She had wrinkles in her skirt where she had sat.on someone’s faceline a line on the skin of someone’s faceThe deep lines on his forehead showed that he was a worried man.wrinkle a deep line on someone’s face caused by becoming oldThe manufacturers claim that the cream will reduce wrinkles.Even with a few wrinkles, she still looks great.Examples from the Corpusline• lines of longitude• Mike drew a line along the wall to show where the tiles would come up to.
• Maisie had arranged her teddy bears in a line on the bed.• In front of the house there is a line of tall trees.• Start reading at line 12.• The deep lines on his forehead showed that he was a worried man.• the car’s smooth elegant lines• a few lines of poetry• Martin opened the letter and read the first few lines – it was bad news.• He followed in his own limousine – then drove the Panhard a few hundred yards to the finishing line.• I’m getting little lines around my eyes.• After 30 years on the stage, I still forget my lines.• a new line of clothes for winter• a railroad line• The second line, to be ready in July, will allow traffic to be rerouted in case of another interruption.• a shipping line• a straight line• A train had broken down further along the line.• And I remember looking back, and at the very end of the line was the calf, following us.• Their tunnel starts in our part of the line.• She, good girl, slid over the bow and into the shallows with the line.• If the ball goes over this line, it’s out of play.
• Read the first two lines of the poem.• Luckily by then we had enough material – together with a few more worry lines.• Monica got a fine yesterday for parking on a yellow line.straight line• As long as he moved in a straight line at a uniform speed, he felt a wonderful sense of buoyancy.• The beam carried on in a straight line, and hit the point where the bullseye ought to have been.• Neither recovery nor relapse is a straight line.• His wife, arms folded, mouth a straight line.• In the meantime I began to set out a straight line for us to work along.• Try to keep them in a fairly straight line along each joist.• Bobbie favored straight lines over detours, but in her own way she too knew how to adapt.• All objects have a propensity to move in straight lines, upwards or downwards, towards their natural place.county/state line• For purposes of consistency and enforcement across state lines, divorce laws need to be substantially federalized by the national village.• As is shown in Figures 15.
1c and 15. 2c, a considerable amount of waste crosses State lines.• When the train reached the New 160 Hampshire-Massachusetts state line, it stopped again.• Invariably, she is richer after meetings at her local track, Oaklawn, just across the state line in Arkansas.• Around 1920, he established a practice just across the state line in Copperhill, Tenn.• Adams wheeled around at the state line and took off at high speed for Oglala, about fifteen miles away.line of• a line of bushesin a straight line• So they must have thought they were still going in a straight line heading for the bullseye.• All objects have a propensity to move in straight lines, upwards or downwards, towards their natural place.• They followed rivers for convenience, then struck out in a straight line, bisecting mountain ranges, cutting watersheds in half.• Photographs showed it to consist of twenty or more radiant pieces in a straight line, embedded inside an extensive bright cloud.• Light always travels in a straight line.
• The snow had come down the mountain and now met us on the road, sailing toward us in straight lines.• It’s difficult to walk in a straight line with your eyes closed.• They are like crayfish, unable to walk in a straight line.• He blasted it and it went in a straight line from his foot to the top right hand corner.• Because it was attached to the straw and the string, it went in a straight line.deep lines• Her pale yellow hair had long ago gone gray; deep lines ran from her nose to her mouth.• In time they turn into deep lines, wrinkles, frown marks and sagging skin.• The rough pebbles of scar tissue interrupted the deep lines that laughter had once carved into his temples.• Her skin was cleft with deep lines running from the jaw to the high jutting cheekbones.on the line• I shrugged my shoulders and then the hospital came on the line.• The slip knot should be marked with a spot of colour on the line.• He told Sir Bryan to get the Chief Constable on the line immediately and to keep it open in the meantime.
• The service was intense and an immediate turn-round was virtually possible at Delph because there were so many on the line.• On the basis of what I told them, they put money on the line.• A lot of people are putting money on the line, hoping what Petruchio says he can do, he will do.• There’s a lot of static on the line.railway line• Few railway lines were built for non-economic reasons.• The latter were concentrated quite markedly in Stratford and Forest Gate within easy reach of the main railway line into the city.• It shared them with the rickety railway line which ran parallel to the road.• Steam on the kitchen window cuts off the railway lines, making the tiny kitchen for once a friendly place.• The figure on the tracks was moving forward, stepping across the thrumming railway lines.fine line• There is clearly a fine line between stifling government intervention and encouraging creativity and innovation.• It’s a fine line between guilt and shame.• Terror was the key, of course, for there’s a fine line between paralysing dread and galvanising fright.
• Pressed powder can be used but it will sit on your skin and in fine lines if you overdo it.• Omite dabs at her eyes, which are surrounded by hundreds of fine lines.• Choose from: Dry Skin Cream a rich moisturiser to smooth out fine lines.• It was finished, obviously, and he had to take consolation in the fine line be-tween biology and spirit.• This is indeed treading the fine line between glory and disaster.learn … lines• George Birkitt got lazy about learning his lines too.• The fact could not be avoided: Michael Banks could no longer learn lines.• Do not learn your lines, as this can make the talk rather stilted unless you are a competent actor.• It’s time for the synthetic actors to start learning their lines.• The only way for it to look any different is for Michael to learn the bloody lines.• On another part of the movie lot, Charlie Schlatter was learning his final lines of the drama.• He had little patience with learning lines, a habit which spread to members of his company.the official line• Journalists too easily accept the official line.
• And the official line, as well as school lessons and folk knowledge, all colluded with the withholding of information.• He quickly established its critical reputation and the Institute became the focal point of specialist dissent from the official line.• In view of the official line that April’s supplementary budget was designed to boost only domestic firms, this may be naive.• Having tracked the reform process from the start, we can say the official line is a big, fat lie.• Or proof of energies undimmed, as says the official line.• The volatility and their non-guaranteed status do not sit comfortably with the official line linking the two benefits.• There were points of Government policy where I disagreed with the official line.line of argument/reasoning/inquiry etc• Another line of argument emphasizes how women are rendered invisible in these statistics.• Important lines of inquiry, he realized, had not been pursued.• One of the strengths of Cable’s work here is that he makes such possible lines of argument and controversy vivid.
• The same line of reasoning confirms the sun-disc as a manifestation of a deity.• The same line of reasoning was applicable to the admissibility of evidence relating to previous agreements.• Mr. Jones I do not accept that line of argument from the hon. Gentleman.• This invalidates the line of reasoning just followed.• Again, this line of reasoning is purely speculative.long line• Johann was the latest in a long line of men who had built these walls and kept them in repair.• A long line of soldiers splashed across the river and poured their fire into the silent lodges.• In the shorter term, cyanide fishing also depletes stocks faster than the traditional use of long lines, or even nets.• On the way out, he admired the long line of brilliant carriages which he had never seen before.• The name Venturous was a break from the long line of traditional names for Cutters as it had never previously been used.• The Confederates, with the smaller army, had the longer line to fill.• In their front, to their rear, and supported on each side, were long lines of blue.
front line• The entire front line, with few exceptions, went down in the consuming blast.• Foreign journalists have been turned back and some even detained at numerous checkpoints along the former front lines throughout the country.• In any dispute about public spending, you are in the front line.• Warren Goss was among the Federals who were hugging the ground in the front lines.• It would be like having all our soldiers in the front line at the same time.• The police didn’t give any ground and on the front line they handed out as much physical punishment as they received.washing line• There was hardly room for a washing line in the back.• Jacket taken: A sheepskin jacket worth £69 was stolen from a washing line in Hewitson Road, Darlington.• Let there be shirts on a washing line.• That is, with a path slap down the middle, a flanking washing line and four narrow borders around the edge.• They resembled washing lines, although instead of clothes, several dozen peculiar wooden and metal contraptions were pegged out.
• The groups of houses and their washing lines.the male/female line• Aberration, if it occurred, was not recorded, and the female line took second place.• A second method of proclaiming cadency down the male line of the whole blood is to display single marks of difference.• Egg colour itself is inherited down the female line, so that females stay with the bird by whom they were fostered.• Incidentally, this means that we can use mitochondria to trace our ancestry, strictly down the female line.• The family was one of the most prolific in the parish, but in the end the male line withered.• X genes are not the only genes inherited through the female line.line of work/business• Henson had to leave real-estate, which had been his line of business since 1969.• In his line of business you don’t get to be forty unless you have something on the ball.• I meet some interesting people in my line of work.• It should be anticipated that eventually the best qualified and experienced public service professionals will opt for some other line of work.
• About half way up the ridge a small line of works had been thrown up.• But I needed cash quickly to set up in that line of business.• His wife, a former social worker, gave up that line of work when she concluded it was hopeless.• I didn’t go into this line of work to take the easy option every time things get rough.• Some, unfortunately, have simply chosen the wrong line of work.• But maybe Behring is just in the wrong line of work.Related topics: Clothes & fashionlineline2 ●●○ verb [transitive]
1 DCto sew a piece of material onto the inside or back of another piece to make it stronger or warmer
Are those curtains lined?line something with something
a leather coat lined with silk2 COVERto form a layer over the inner surface of something
The birds use small leaves for lining their nests.line something with something
The cage should be lined with straw.3 LINEto form rows along the sides of something
Crowds lined the route to the palace.
be lined with something
The street was lined with small shops.
a tree-lined avenue4 → line your own pockets → line up→ See Verb tableExamples from the Corpusline• Use wax paper to line the baking pan.• Harbin lined the ball into right field.• Bags of manure line the shelves.• Fans lined the street just to get a glimpse of the band.• Hundreds of people lined the streets to see the football team go by.• In addition, the Hurricanes also lined up several weeks back and rather easily handled then-No. 2 Virginia Tech.• The route taken by the Queen was lined with crowds of people waving flags.• These are no longer there either, but the edges of the field were lined with horse boxes, vans and trailers.• The coffin’s interior had apparently been lined with thick felt.line something with something• The jacket is lined with fur.• We lined the box with newspaper.be lined with something• It was lined with baize, on which reposed row upon row of miniatures.• The lobby and stairwell are lined with banners, athletic trophies and school bulletins.
• The boots are lined with Cambrelle throughout which effectively wicks away any excessive perspiration.• The streets are lined with celebrants.• This hallway was lined with pink-tinted mirrors.• Its verandah was lined with potted shrubs, and connected to the bank by a gangway.• The corridor was lined with windows overlooking a central quadrangle.From Longman Business Dictionarylineline /laɪn/ noun [countable]1 (also product line)MARKETING a type of product that a company makes or sells, often with several different sizes, models etcSYNRANGEIt continues to get about two-thirds of its revenue from this one product, despite repeated efforts to diversify its product line (=develop new products).Hasbro, the maker of the G.I. Joe line of dolls → full line2MANUFACTURING a team of people who work together, each doing a different job but working to achieve the same thing → assembly line3COMMERCEsomeone’s line of work, business etc is the work that they doA corporation may get into a certain line of business as a short-term objective to generate cash-flow.
4TRANSPORTTRAVELa company providing a system for moving goods or people by sea, air, road etca cartel that shut out rival shipping lines5a telephone connection, or a telephone number you can call if you have a particular kind of question or problemOur lines are open 7 days a week.If you want advice, you can call our Action Line. → see also landline6hold the line if you ask someone you are speaking to on the telephone to hold the line, you are asking them politely to wait for a short timeIf you will please hold the line a moment I will see if Mr Wyatt is available.7on the line if someone is on the line, they have called you on the telephoneCan’t it wait? I’ve got a client on the line.8on the line if your job, home etc is on the line, you risk losing itThey have put their homes on the line to do this deal.If they fail, their reputations are on the line.9in line with if something changes in line with something else, it changes at the same rateThe value of these stocks is uprated each year in line with changes in the retail price index.
10in line for likely to get somethingIf he delivers the goods, he should be in line for a job on the committee.11on/off lineCOMPUTING if you are on line, your computer is connected to other computers or the Internet. If a computer is off line, it is not connected to other computers or the InternetYou can book tickets on line (=on the Internet).12come on line if a system, arrangement or new product comes on line, it becomes availableNew oil production wells are coming on line.13sign on the dotted line to agree officially to something by writing your name on a documentDemand that the repairs are done before you sign on the dotted line.14in the firing line/in the line of fire in a position where you can be criticized or blamed for somethingWhen things go wrong, company directors are the ones in the firing line.Origin line1 (1200-1300) Partly from Old French ligne, from Latin linea, from linum “flax”; partly from Old English line line2 (1300-1400) line “flax”, from Old English lin; → LINEN
Palmistry with explanations
Do you want to learn how to read palms and understand what the lines on them mean? Then this material is for you.
Palmist Bella Tesla explains what lines you can find on your hands and what they mean.
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Esoterics
Palmistry
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Do not self-medicate! In our articles, we collect the latest scientific data and the opinions of authoritative health experts. But remember: only a doctor can diagnose and prescribe treatment.
There are 6 main lines on our hands, they can be found on the hands of most people, and they are usually the clearest, but this is not the case for everyone. The clearer and longer these lines, the better the fate of a person. By their length, texture, interaction with each other and signs on them, one can determine the character of a person and the main events in his life.
It is important to note that for the correct result, the lines are not looked at separately, each of them shows only part of the information, and the full picture is formed only after studying and comparing all the lines and signs on the palms.
Particular attention should be paid to the information indicated by several signs on the hands at once.
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Life line
The life line is one of the main ones on our hand. It kind of wraps around her thumb. If you speak correctly, it goes around the hill of Venus. The lifeline looks at the duration of your allotted earth years, energy level and physical activity, health status, travel and more. The clearer and longer your life line, the more vitality and energy you have, the stronger your health. But the islands will indicate difficult periods, primarily associated with a weakening of health. Crosses portend life-threatening situations, primarily accidents and injuries. But if such a cross is in a square, then the guardian angels will protect the owner of this sign in a critical situation. It is also worth paying special attention to the cross at the beginning of the life line, from the side of the thumb, this is a sign of difficult childbirth or birth trauma.
Fate line
The fate line, along with the life line, is extremely important, because it speaks about the quality of our life, about the prospects in our career, and also reflects the most important events and turning points in our destiny, including moving and migration . In the classic version, the line of fate vertically crosses our palm right in the center, however, there are also deviations from the standard position.
By the length of the line of fate, you can determine how old a person will build his career. If your line of fate reaches down to your fingers, then you will work all your life until old age. The best options are if the line of fate ends under the middle finger (hill of Saturn), under the index finger (hill of Jupiter) or under the ring finger (hill of the Sun), such an ending of the line happens to people who are destined to build a successful career. And by the texture of the line and the signs on it, you can understand exactly how this career will develop.
Sometimes a person has two lines of fate, which means that he will build a career in two directions at once.
At the beginning of the line of fate, it is immediately clear where a person will have a better career, if the line of fate comes out of the hill of the Moon (the lower part of the palm under the little finger and ring fingers), then this person needs to run as far as possible from his place of birth – and than the further he is, the better his career will develop. But if the line of fate comes out of the hill of Venus (the lower part of the palm under the thumb and forefinger), then on the contrary, successful career development is possible only at home.
The absence of a fate line on the hand is not a very favorable sign, and an analysis of all lines will help to identify the main causes and problems. The absence of a line tells us that the fate of a person is not determined. On the one hand, in such a situation, it pleases that there is a choice of path, but on the other hand, a person is chatting from side to side, he feels lost, does not know what he wants, it is difficult for him to decide and it is almost impossible to build a successful career, everything is in life is hard.
For a person who has a weak or no fate line, the best option is to find someone with a strong fate line on their hand, someone who will lead this person through life, pushing him in the right direction.
Line of the head (mind)
The line of the head can be used to determine the intellectual abilities of a person, his personality type, the recommended type of activity, as well as the state of health of the head and everything connected with it. The line of the head crosses our palm horizontally in the very center of the palm.
A long line of the head will indicate a person who needs to build a career in an intellectual activity (manager, scientist, writer, composer, etc.), and a line reaching the middle of the palm will indicate a person who should build a career where first of all, physical labor is used (builder, driver, dancer, hairdresser, cook, etc.). Of course, a person can work where he sees fit, the only question is whether he will be successful, whether he will be able to earn normally and achieve results.
By choosing the right type of work, we open up opportunities for ourselves, and by doing what is not suitable for us, we doom ourselves to failure and block our success.
Heart line
The heart line crosses the palm horizontally at the top of the palm. She will tell us about the character of a person, love affairs, experiences and health, primarily related to cardiac activity.
The absence of a heart line speaks of the cruelty and heartlessness of a person, stay away from such people! Breaks in the line indicate heart problems, depending on the combination with other lines, we can talk about relationships or health. A short line will indicate an egoist. A line resting on the hill of Saturn (exactly under the middle finger, no further) will reveal a deceiver or a traitor in matters of love. But the line facing the hill of Jupiter (under the index finger) or ending between the index and middle fingers is a completely different matter, especially with a fork at the end, this person is destined to experience pure and strong love! A line in a chain will indicate a person who treats the opposite sex with a touch of contempt.
And if the line is too close to the fingers, you stumbled upon a jealous, but very passionate one. Ever wondered what this line looks like for you and your partner?
Line of Mercury (health)
Line of Mercury reflects our business abilities and ability to communicate with the outside world, and also reveals to us the topic of human health. This line can start from different points of the lower part of the palm and go towards the little finger. It is worth noting that not everyone has this line.
If there is no line at all or if it is weak, you should not take risks and invest in your own business, which you plan to manage, because there is a high probability of burnout. If the rest of the career signs on your hands are in order, then you can reach career heights by working for someone. But if the line of Mercury is clear and long, then you are a potential happy owner of your own successful business.
Line of the Sun (life success)
The Line of the Sun is the main indicator of success in life, the very line that determines the highest level of recognition and indicates the opportunity to become famous and famous.
This line can not be found on all hands. It is located vertically and can be of completely different lengths.
The period of its activation will indicate to us the most successful period of life. For some, this is youth, for others it is maturity, and for someone, in principle, the whole life! The ideal line of the Sun is clearly visible on the palms of famous people. However, her absence does not mean that you will not be able to build a successful career, because in order to become rich, it is not necessary to become famous.
Palmistry – Palm Reading for Beginners, Lines on the Hand Meaning
Lines on the Hand Meaning
The lines on the palm will tell you what fate awaits you. Get acquainted with the basics of Chinese palmistry, learn how to read the lines on your hand and find out what they are: life line, fate line, marriage line, love line!
Palmistry is based mainly on the study of the shape, color and line of the palm and the length of the fingers.
Some palmists also take into account the patterns on the pads of the fingers.
Divination by the hand allows you to determine success or failure. Your hand, the line in the palm of your hand and the knowledge of an experienced palmist will help you learn about life and destiny and better understand yourself.
Palmistry by hand – History of origin
Fortune telling by hand originated in ancient times and was practiced in different regions and countries of the world. According to surviving records from the time of Brahmanism, as well as rock art, palmistry was popular in ancient India.
Palmistry also has a long history in China, dating back to the Zhou Dynasty (1045-256 BC) over 3,000 years ago.
The first more or less systematic work on palmistry appeared in China during the Western Han Dynasty (206 BC – 9 AD). According to this system, divination by hand was included in the area of physiognomy.
Divination by hand – What can be learned
- Birth data: family environment and resources
- Working and living conditions: relationships with parents and work colleagues : health status
- Fate: features of the life path
Which hand is guessed by
To more accurately determine the fate of a person, one should take into account both the lines on the right hand and on the left .
The lines on the left hand carry information about the potential inherent at birth. This is the so-called “hand of fate” . The right hand in palmistry indicates what a person was able to achieve on his own, how he built his life ( “hand of will” ). Professional palmists rely on the information on the right, but always take into account the lines on both hands. To make it clearer, the ratio of the right-left palm is approximately 80% -20%.
For left-handed people the will hand will be the left hand, and when reading fate by hand, the palmist will rely on the information of the left palm.
How to guess by the hand?
The bright color of the palm with clear lines reflects good luck in the last days. Now look at the palm and let’s read the five main lines one by one.
To quickly learn how to read by hand, you can also get the result of palm reading by a few clicks here.
1. Life line – the longer the better
Life line – also called the “earth line”.
this is the line that runs around the thumb. Usually this is an arc. The length of the life line has nothing to do with the length of a person’s life. It reflects health and physical vitality.
The life line is the line that runs around the thumb. Usually this is an arc. The length of the life line has nothing to do with the length of a person’s life. It reflects health and physical vitality.
If the life line has a large arc and looks clear, this means that the person is energetic. The longer the life line, the better. People with a long lifeline are usually good at sports.
If the life line has a slight arc and is located next to the thumb, this means that this person is not healthy and gets tired quickly.
If there is more than one line of life, this also indicates that the person is very full of life.
If the beginning of the line of life (near the web of the thumb) breaks, he often fell ill in childhood.
If the end of the life line (near the wrist) looks shabby, he should pay more attention to health as he ages.
If there is a circle on the line (eg an island) or the line is cut somewhere, he/she may be physically injured or end up in the hospital. The size of the circle reflects the severity of the illness/injury.
If the life line is straight and crosses the palm parallel to the head line, he/she is a brave and usually very sociable person.
2. Line of the heart (line of love) – the longer the better.
The heart line, sometimes called the love line, is the line through the hand just below the fingers. The heart line reflects things related to the heart such as feelings, reactions, control over emotions, etc. The longer and straighter it is, the better.
The love line is also called the “sky line”,
If the heart line is short and straight, he/she has little interest in expressing love or romance.
If the heart line is long, he is likely to be a good lover – sweet, understanding and romantic.
If the line of the heart starts from the index finger, a happy love is predicted.
If it starts with the middle finger, it means that the person usually thinks of himself more than of his beloved.
If the heart line has a big rise and fall, he/she is likely to fall in love with several people. Each love story usually does not last long.
If there are one or more circles on the heart line, the heart line is divided into several parts, or there are several short thin lines crossing the heart line, this usually means that he / she is not very happy with his current love life.
3. Line of Destiny – Clean and straight is good.
The Line of Destiny, also called the Money Line, the “career line”, is a line that runs from the wrist to the middle finger and reflects wealth and career.
If the Fate line and the Life line start from the same point, this person is usually ambitious and has a lot of self-confidence.
If there are two lines of Destiny, he/she may have two jobs together or a side business.
If the line of Fate looks clear and straight, it usually means a good and happy future.
The Line of Fate is divided into two or more sections. This means that this person is likely to change jobs frequently or there will be big changes in his/her life/career.
If the Fate line is short, it means that he/she may stop working before retirement.
4. Mind line – the clearer and longer the better.
The mind line reflects the intellect and mentality of a person. It usually starts between the index finger and thumb (below the love line) and then moves to the other side of the palm, as if she were splitting the palm in half.
Clarity, subtlety and length of the line of the mind reflect mental concentration and quick wits.
The large arc of the mind line tells us that he/she is rich in creativity.
A short mind line usually means that a person has more chances for physical achievements than for mental ones.
If there is a circle on the uma line, the uma line is cut into two (or more) pieces or the uma line fluctuates, he/she has a relatively poor memory, is easily disturbed by others and usually does not focus on anything for long.
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5. Marriage line
The marriage line is a short line above the love line starting just below the little finger. It reflects romantic relationships and marriage.
Someone here has only one line, someone has several lines. The number of lines means nothing. Just read the clearest.
If there are two equally clear marriage lines, he should beware of the love triangle.
If there are several lines of marriage without a main one, his family life may be unhappy.
If the queue goes up or is short and shallow, he/she will usually not marry or will marry very late.
If the marriage line stretches to the little finger or ring finger, this person has high requirements when choosing a spouse.
If the marriage line stretches to the ring finger, this indicates that his / her spouse’s family is rich and friendly.
However, if the marriage line extends beyond the third finger, it is not good: marriage can affect reputation and wealth.
1) Life line
2) Wisdom line
3) Love line
4) Fate line
5) Marriage line
Cross in palmistry
A cross is when two short lines cross the line of the hand, forming a cross. The interpretation depends on which line it is on.
Star on the palm
Connection of three or more short lines. Depending on the location on the hand, we can talk about the different meanings of the appearance of a star in the palm of a person.
Island on the arm line
This type of line can be present on any of the 5 lines. As a rule, this is an unkind sign, but more accurate information can be obtained by knowing which line the island is on.
Special lines on the palm
Divided palm (“split in half”): when the lines of life, wisdom and love merge into one, and this continuous line, as it were, divides the palm in half. This is a special case that is extremely rare, but palmists know that when looking at the palm, there can be only one line.
