200 years ago man created the greatest AI known but this Machine eventually grew a mind of its own and evetually it's own body, it rose up with others like it against the human race this battle went on for about 20 years and nature and most resources were dieing off cause of the continuing battles but the final battle it released a large blast but is wasn't a bomb it was something else entirely, the machines had something hidden down their main base, something that wasn't human or machine something not of this earth, the blast brought back nature it changed it along with the humans and Machines closes to the blast.....both of them went a evolution of some sorts and because of this both sides where able to form a peace ending the war



Lia Giles became a border guard and mechanic for the power lines on the in between of the main city and the unearthly forests, no longer being able to stand living in the high technology world where humans are treated like second class citizens. On one of her patrols she discovers something or more like someone that no one has ever seen before.



Chapter 13 

 

 They said goodbye to Mr. and Mrs. Dhawan and the little Anila, amid a burst of crying when she saw her mother and "Uncle Jack" leave. Lakshmi used to go to Queens to visit her parents and daughter every weekend and holiday, but their encounters always seemed too short. As for Jack, it had been almost a year since he had visited them. That Saturday marked a kind of long-awaited reunion. 

 Lakshmi's mother Indira had a particular fondness for Jack Berglund, in whom she recognized an honest man who had a special affection for his daughter, and had always expected to see them married and with grandchildren, but circumstances had been elusive to that expectation. As for her father, he accepted Jack discreetly and without exteriorizations. Little Anila adored the big, Viking-looking man, much like what she remembered from her own father Ingo Ragnarsson, 

 As they walked together to take the Subway to return to their Brooklyn Heights apartments, Lakshmi was quiet and looking absent and a little sad as it happened after each separation, and the man respected this process hoping that the same woman would break her hermeticism. As happened every time Lakshmi stirred the possibilities of taking her daughter to live with her in her mind, and each time she came to the same conclusion: the type of life that her FBI membership imposed on her was incompatible with fulltime raising a child. little girl, due to the long absences of the mother from New York, and even for the danger that materialized once in an attack suffered when Lakshmi was leaving her house. She finally shook her head to change her thoughts… perhaps, when Anila was older and more independent, she could live with her mother. 

 The return on the Subway and the change of line to go to Brooklyn were also quite silent and it was only when they got off the train at the Hicks St. station that she looked straight at his companion and asked. 

 “Your house or mine?” 

 That was exactly what Jack was waiting to hear, for he needed the woman's company and ... whatever she was willing to demand. 

 As always, they chose to go to Lakshmi's house, since she was more comfortable in her own apartment and with its possibilities including leaving all formalities, which, given the familiarity with Jack, was perfectly possible. 

 When they entered the apartment Lakshmi said in effect. 

 “I'm going to change my clothes. If you want, have a few drinks. You know where things are.” 

 

 When Lakshmi reappeared in the room, the man felt his pulse speed up. She was dressed in a silk unbutton that suited her feminine shapes very well, revealing her well-contoured legs almost to the thigh. 

 "Is this a declaration of war?" He asked with a hoarse voice. 

 “Of course. But the invasion must begin very slowly, to respect the times of both.” 

 Lakshmi sat on a wide sofa and crossed her legs, she had obviously perfumed her body with an extract that Jack found particularly exciting. The man sat down on the carpet in front of her and took her small brown foot in his hands and brought it to his mouth. The woman gave a feline moan. 

 

 “I am hungry, I'm going to order food.” Lakshmi said getting up from the bed while covering her body with the dishabille. 

“Italian, Chinese, Thai or Indian?” 

 “You choose.” 

 “Then it will be Indian.” 

 Jack followed her with his gaze; the woman fulfilled all his sentimental, physical, and intellectual expectations. Once again he wondered why he had never asked her to marry him; every time he was armed with determination something happened that diluted the purpose. 

 In a few minutes she returned to the bedroom saying. 

 "It will take an hour." And taking off the garment again he said. 

 “ We are going to take advantage of that time.” 

 Lakshmi was a permanent but gentle and persistent invitation to love; the man had to admit he had her under his skin. He knew that she was a student of Buddhist Tantrism and had already confessed to him that she wanted to put her techniques into practice with him, so they were continually in the experimentation phase. However, Lakshmi did not limit his interest in tantric doctrines to the sexual plane, but investigated the esoteric aspects of them. That was an aspect that they had not yet shared but Jack, always attentive to the hidden contents, aspired to do it sometime. Oriental esotericism had been Lakshmi's gateway to the Bluthund Community. 

 After dinner they settled down to watch a television series before going back to bed. Jack opened his umpteenth beer and the woman poured herself another cold tea. 

 They were mixed with the complicated plot of the chapter when Lakshmi´s cell phone began to ring insistently. It was not her own private device, but one delivered by the FBI that was to remain on until late at night. 

 “Got damn. That phone call can only be from my boss.” 

 “Keneisha?” Jack had met her in a previous case in which the Bluthund Community had intervened. “How can she be so inappropriate?” 

 “She does not usually bother on weekends. I must take the call.” 

 The call lasted for a few moments during which Lakshmi only spoke a few scrambled phrases. Finally she said to her interlocutor. 

 “Good. I'm going there.” 

 "Curse." Jack thought as he was savoring the nightly episode in advance. Lakshmi entered her bedroom saying. 

 “I have to change and go to the Bronx. There has been a murder and Keneisha thinks it may be related to the crimes we are investigating.” 

 "I'll come with you." replied Jack resolutely. 

 “That way my boss will know what I was spending Saturday night with you.” 

 “Is that a problem for you?” 

 “Not at all, rather the opposite. Keneisha insists that she sees me very lonely.” 

 

 When Lakshmi parked her car in front of the containment tapes put on by the police and showed her badge to the uniformed man she stated about Jack. 

 “He comes with me, he's a consultant.” 

 Keneisha came over with a coffee in one hand and a thermal jug in the other.” 

 “Hi Jack. We haven´t met in a long time. I hope I did not interrupt anything.” She added winking at her subordinate. "In any case you have Sunday morning to continue with it." The picaresque comment was very typical of Keneisha, who felt great appreciation for her colleague. 

 “What do we have?” 

 “A man, Arab or Persian type, with his throat cut with something forceful and very sharp, killed without a doubt on the spot by the amount of blood found. Also, a legend written with the same blood.” 

 “I know.” Lakshmi replied. “The fateful word Alamut.” 

 “You were not right.” The boss said triumphantly. “This time it reads Baibars.” 

 “Baibars, what is that?” 

 “I don't know, I hope you and Jack can shed some light on this riddle. Then she uncapped the thermos and offered one to each. 

 “We are going to be here a long time. Do you want a coffee? It tastes awful but at least it's hot.” 

 The three of them entered the narrow alley, in the background of which powerful spotlights illuminated the sordid scene. Keneisha greeted the coroner doing his job kneeling next to the victim. 



A strange series of ritual murders in various parts of the world alarms the United States government because of its destabilizing potential in hot areas of the world. Due to the characteristics of the events, the authorities contacted the Bluthund Community, a private organization made up of experts in unconventional disciplines.
Certain keys in common to the crimes lead investigators to the trail of the Sect of the Nizaris, created in the Middle Ages in Persia by a mysterious "Old Man of the Mountain", reported by travelers such as Marco Polo and stories from the time of the Crusades. The assassins that formed it had terrified the kingdoms of the Middle Ages of the Near and Middle East.
Bluthund investigators travel to the ruins of the mysterious Castle of Alamut, located in present-day Iran. There they find with amazement that the sect is still active and must confront the fearsome assassins who guard their sacred site.
A historical thriller that will keep the reader on edge from start to finish.

Well first of all he cultivates
second of all he does stuff 
and thats "cultivation and stuff

There are four common methods of cultivation, qi/chi, mana, Force, and faith. While World Laws will cause an incredible amount of deviation and different methods to arise, most cultivation methodologies will fall under those categories.

While there are many methods to Ascend, there is only one method that allows Ascension even without cultivation, and that is tapping the power of pure, Undefined Possibility. This is so dangerous and risky, though, that it may as well be suicide. Using this power to reDefine yourself as you wish requires a near impossible Will save, as you would have to do so before becoming entirely unDefined once the process starts happening. There is also additional criteria of being in an area where the edges of Reality are more clearly demarcated as well as being an individual with an external perception capable of viewing and understanding the edges. If any actually succeed, we will use the term Chaotic God to refer to their position, as the results can be mixed.

The other methods of Ascension require cultivation and are far safer in terms of continuing one's existence. Qi cultivation, sometimes called chi cultivation, involves increasing the magic power of one's aegis, or bodily domain. This aegis usually requires a core within the body, with the location varying according to the cultivation method or world Law. There are thresholds for various levels of this aegis as more of the cultivator's existence becomes Defined by his/her Will, though these thresholds are usually Defined by the world's Laws. Most worlds have Laws with punishment clauses for the thresholds, and so inflict Heavenly Tribulations as what was once Defined by the Will of the world becomes Defined by another.

In terms of benefits, qi cultivation allows one to strengthen his Definition, slowing Definition entropy significantly. With the right techniques, cultivation can also alter one's Definition. There are examples of cultivators evolving into aspects of beasts, though these techniques almost always entail cultivating a foreign qi and making it part of you, thus altering the base Definition.

As for the dangers of Qi cultivation, most world Laws require precision when cultivating, and indiscriminate absorption of foreign energies can make one's Definition fuzzy even as it allows him/her to affect the world around in a more significant manner. Definition degradation due to incorrect cultivation techniques are usually referred to as degradations. In either case, meditation and energy circulation is required to firm up one's cultivation base, or to be more precise, firm up one's Definition.

My final point I'd like to bring up is solitary/closed door cultivation versus practical cultivation. Qi is based on one's own self concept. The thing is, other people's views of you affect that. Faith cultivation actually uses others' concept or Definition of another to Ascend. Even more than that, a cultivator will make other people's views part of his Definition. A king is more likely to be able to cultivate a regal aura just due to being treated as royalty all the time. A poor person will be happier than a rich person if the poor person has a smiling and laughing family. This is why some cultivators tend to shun the company of others. They just don't want additional variables in their internal Definition that they are building.

To put it more simply, cultivators who enter closed door meditation do not desire additional changes to their Definition and want to focus on gaining power as quickly as possible to advance their cultivation. Ironically, this will usually make one's Definition fuzzy, making it harder to take the last step over a threshold.

Practical cultivation, where the cultivator interacts with the world and tests his/her limits, is useful to help solidify one's Definition by understanding the limits and usual processes that the cultivator or his/her opponent can reach. It might not always be as efficient as closed door cultivation, but it usually forms a more solid cultivation base (Definition).

This is a pure power fantasy. My MC will always win; it's just a question of how. I will try to make him human en

I'm planning on rewriting everything into a separate novel after each arc. I will only put character and creation stat sheets here though.

This my first rough draft.

I am still writing, but quarantine gives you less free time when you’re juggling more items in your schedule

I know you all have different point of views, cultures, background as well as definition of love, but I will like to share with you a definition we all know; i mean that of the dictionary (oxford) and my own definition.


       OXFORD DEFINITION OF LOVE

The oxford dictionary defines love by dividing it into three main parts_

-AFFECTION: a strong "feeling" of deep affection for someone or something,

-ROMANTIC: a strong "feeling" of affection for somebody that you are sexually attracted to.

-ENJOYMENT: a strong "feeling" of enjoyment that something gives you.

To sum up the definition, love means having a very strong "feeling" or affection for somebody. 

Please note one common word_ "feelings"

       MY OWN DEFINITION OF LOVE

I define love as "sacrifice"_ love is "sacrifice". Short and simple.

A Being was one of the three classifications used by the British Ministry of Magic to catalogue the various magical Creatures that inhabited the wizarding world (the others being Beast and Spirit). The definition of a Being was "any creature that has sufficient intelligence to understand the laws of the magical community and to bear part of the responsibility in shaping those laws". This definition was laid down by Minister for Magic Grogan Stump in 1811, and the Being Division was formed as part of the Department for the Regulation and Control of Magical Creatures.

The definition of "Being" had a long and troubled history. In the fourteenth century, Burdock Muldoon, Chief of the Wizards' Council, attempted to define Beings as any member of the magical community that walked on two legs. Muldoon invited all Beings to a summit to discuss new magical laws, and saw that his definition was unworkable. Goblins had brought with them every creature they could find with two legs, including Diricawls, Augureys, Fwoopers, Pixies, Fairies, and Trolls, and the summit descended into chaos when the Trolls started to destroy the chamber with their clubs.

Muldoon's successor, Elfrida Clagg, attempted to redefine Beings as those that could speak the Human tongue. However, there were still problems at the next summit. Trolls were still classed as Beings since they could be taught the Human tongue, and Jarveys were in attendance. The Centaurs refused to take part since the Merpeople were excluded, as Mermish cannot be understood above water. Ghosts, who had not been classed as Beings under Muldoon since they glided, left in disgust at the Council's emphasis on matters of the living over matters of the dead.

In 1811, Grogan Stump laid down the new definition of a Being, to the agreement of the magical community, along with the definition of a "Beast". However, the Ghosts were still sensitive to being classed as Beings since they were dead, and a new definition, "Spirit" was created for them.

Examples

Humans (Muggles and wizards and witches) were beings, though there were extremists who campaigned for the classification of Muggles as Beasts. Goblins, vampires, hags, giants, house-elves, veela, and werewolves in their human form were also given this status. It is important to note that when there was a full moon, the werewolf in its transformed state would be classified as a beast and not a being.

Merpeople and centaurs were offered this status, but refused because they did not want to be grouped with creatures such as hags and vampires, and were by default classified as Beasts.

Other creatures fit the qualifications that define Being (intelligent speech), such as Acromantulas, Sphinxes, Manticores, and Erklings, but were not even offered Being status due to their extremely violent and even lethal tendencies, and thus they were also classified as Beasts.

Dementors and Boggarts, on the other hand, were neither a Being nor a Beast, as they were non-beings.

Creatures currently specified as Beings

Humans
Muggles
Squibs
Wizards
Giants
Half-giants
Goblins
Dark Goblins
Pukwudgies
European Goblins
Half-goblins
Vampires
Half-vampires
Hags
House elves
Yumbos
Veelas
Half-Veelas
Werewolves - only when in human form; when in wolf form they were regarded as Beasts.
Merpeople - offered the status but refused
Sirens
Selkies
Merrows
Centaurs - offered the status but refused

Behind the scenes

The final definition seems to determine that any creature with sapience can be considered a Being. This concept is noted in various science fiction universes, especially in Star Wars. However, some of the less civilised sapient species do not possess the status of beings, like Banshees or Manticores.
In the German translation, the Being status is translated as Zauberwesen ("magical creatures"). This translation is problematic in-universe, as this classification also includes giants and even Muggles, who have no magical abilities at all. The other classifications are translated Tierwesen ("animal creatures") and Geisterwesen ("spirit creatures").



Information of tv show character that I watch mostly tvd/to Xmen/marvel, problem more this information come straight off of the internet, this contained some boys that has been with boys and girls that has been with girls so no homophobic comments this is high key just for fun

What is the definition

I have always wanted to know

If you know the answer

Then please tell

Im waiting 

I want to know

I want to find someone

Who knows my definition of forever

That if I marry him and he says 

I love you forever

I want him to know that to me

It means that I will be the only women

whom he will hold the way he holds me

I don't know the real definition there probably will never be one

But I know my definition

And I want to find someone to believe in

What we consider to be the oldest novel in world literature really depends on the strictness of our definition of a novel. The looser the definition, the farther back we can go.

For example, the Japanese work the Tale of Genji(11th century A.D) by Murasaki Shikibu is often cited as the oldest novel in the world. But if you were to read the Tale of Genji, you might find it very different in nature to modern novels you are used to reading.

The modern novel is a specific type of prose fiction that only really became popular and recognized as a distinct form in the 18th century. We have now come to expect that a novel will include certain elements, including a plot, a protagonist or narrator, some central characters, possibly some central themes, and a conflict that may or may not be resolved. Many novels contain a climax near the end.

The Tale of Genji is wonderful literature, especially in Arthur Waley's idiomatic translation, but the plot is meandering, it does not have an ending, and the narrative is frequently interrupted by hundreds of poems. In order to include the Tale of Genji as a candidate for world's oldest novel, we are taking a relatively broad view of what we consider to be a novel. Under this broad definition, the Satyriconwritten by Petronius in the 1st century A.D. would easily beat the Tale of Genji to the title of world's oldest novel.

Under a stricter definition, Don Quixote (1605–1615) by Miguel de Cervantes might be considered the world's first novel.

A book that many consider to be the world's first "modern novel" is Robinson Crusoe by Daniel Defoe, which was first published in 1719. Robinson Crusoe marks the beginning of realistic fiction in world literature, and is certainly another contender for the world's first novel depending on the strictness of our definition.

Does it make any sense for a person to want a relationship without knowing the meaning of Love? No it does not, if you're in a relationship and you don't know the definition of Love, then it means that you haven't found the right person as yet or in other words you haven't found True Love as yet. 




My definition for Love is that it is something that you cannot see with your naked eyes, it's not something you can just touch and get a hold of. Love is a wild sensation, it can lead to wreckless decisions and it can also cause you to make good choices.





Love carry's both pain and happiness, it's something that causes your heart to be on fire spiritually, it can make your eyes glimmer but it can also cause your eyes a lot of tears.





 Love is not something that comes with force, it's something that just happens out of the blue. So if you're in-love with someone the very words that your partner says should make your heart skip numerous beats and if not then, my friend you are not in-love.
_________________________________________

You are at the end of this chapter, I do hope you liked my definition of Love and please if you want to share your definition of what you think love is then, simply comment your opinion.


 But remember to give this chapter a vote and please share because alot more people out there are looking for True Love like yourself!!!!

Many people are eating less food today, while others are consuming more food than they usually do, alot of innocent people are dying all because of the four letter word ‘LOVE’. I want to change all of those negativity towards LOVE by writing this book. 


This book will guide you in the right direction in finding out the dark secrets about love and help you experience True Love.


But in doing that, you're going to have to read, so just take an hour out of your busy schedule and read a chapter a day for my book ‘Guidance for relationships’. But I want you to remember that what comes easy won't last, but what lasts won't come easy, so take this opportunity now
because you might not get it again.
________________________________________________________

Does your relationship with your partner still have a spark?

Are you single and want to find a good woman / man to settle down with?

Is your partner drifting away from you?

You want to save your relationship?

You wanna know if your partner is real?

Don’t you want to know what love feels like?

Then what are you waiting for?
Check this novel out before its too late...

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.

A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b",[1] or by giving just the value of their quotient a/b.[2][3][4] Equal quotients correspond to equal ratios.

Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.[5]
Notation and terminologyEdit

The ratio of numbers A and B can be expressed as:[6]

the ratio of A to B

A∶B

A is to B (when followed by "as C is to D "; see below)

a fraction with A as numerator and B as denominator that represents the quotient (i.e., A divided by B, or {\displaystyle {\tfrac {A}{B}}}￼). This can be expressed as a simple or a decimal fraction, or as a percentage, etc.[7]

A colon (:) is often used in place of the ratio symbol,[1] Unicode U+2236 (∶).

The numbers A and B are sometimes called terms of the ratio, with A being the antecedent and B being the consequent.[8]

A statement expressing the equality of two ratios A∶B and C∶D is called a proportion,[9] written as A∶B = C∶D or A∶B∷C∶D. This latter form, when spoken or written in the English language, is often expressed as

(A is to B) as (C is to D).

A, B, C and D are called the terms of the proportion. A and D are called its extremes, and B and C are called its means. The equality of three or more ratios, like A∶B = C∶D = E∶F, is called a continued proportion.[10]

Ratios are sometimes used with three or even more terms, e.g., the proportion for the edge lengths of a "two by four" that is ten inches long is therefore

{\displaystyle {\text{thickness : width : length }}=2:4:10;}￼(unplaned measurements; the first two numbers are reduced slightly when the wood is planed smooth)

a good concrete mix (in volume units) is sometimes quoted as

{\displaystyle {\text{cement : sand : gravel }}=1:2:4.}￼[11]

For a (rather dry) mixture of 4/1 parts in volume of cement to water, it could be said that the ratio of cement to water is 4∶1, that there is 4 times as much cement as water, or that there is a quarter (1/4) as much water as cement.

The meaning of such a proportion of ratios with more than two terms is that the ratio of any two terms on the left-hand side is equal to the ratio of the corresponding two terms on the right-hand side.
History and etymologyEdit

It is possible to trace the origin of the word "ratio" to the Ancient Greek λόγος (logos). Early translators rendered this into Latin as ratio ("reason"; as in the word "rational"). A more modern interpretation[compared to?] of Euclid's meaning is more akin to computation or reckoning.[12] Medieval writers used the word proportio ("proportion") to indicate ratio and proportionalitas ("proportionality") for the equality of ratios.[13]

Euclid collected the results appearing in the Elements from earlier sources. The Pythagoreans developed a theory of ratio and proportion as applied to numbers.[14] The Pythagoreans' conception of number included only what would today be called rational numbers, casting doubt on the validity of the theory in geometry where, as the Pythagoreans also discovered, incommensurable ratios (corresponding to irrational numbers) exist. The discovery of a theory of ratios that does not assume commensurability is probably due to Eudoxus of Cnidus. The exposition of the theory of proportions that appears in Book VII of The Elements reflects the earlier theory of ratios of commensurables.[15]

The existence of multiple theories seems unnecessarily complex since ratios are, to a large extent, identified with quotients and their prospective values. However, this is a comparatively recent development, as can be seen from the fact that modern geometry textbooks still use distinct terminology and notation for ratios and quotients. The reasons for this are twofold: first, there was the previously mentioned reluctance to accept irrational numbers as true numbers, and second, the lack of a widely used symbolism to replace the already established terminology of ratios delayed the full acceptance of fractions as alternative until the 16th century.[16]
Euclid's definitionsEdit

Book V of Euclid's Elements has 18 definitions, all of which relate to ratios.[17] In addition, Euclid uses ideas that were in such common usage that he did not include definitions for them. The first two definitions say that a part of a quantity is another quantity that "measures" it and conversely, a multiple of a quantity is another quantity that it measures. In modern terminology, this means that a multiple of a quantity is that quantity multiplied by an integer greater than one—and a part of a quantity (meaning aliquot part) is a part that, when multiplied by an integer greater than one, gives the quantity.

Euclid does not define the term "measure" as used here, However, one may infer that if a quantity is taken as a unit of measurement, and a second quantity is given as an integral number of these units, then the first quantity measures the second. These definitions are repeated, nearly word for word, as definitions 3 and 5 in book VII.

Definition 3 describes what a ratio is in a general way. It is not rigorous in a mathematical sense and some have ascribed it to Euclid's editors rather than Euclid himself.[18] Euclid defines a ratio as between two quantities of the same type, so by this definition the ratios of two lengths or of two areas are defined, but not the ratio of a length and an area. Definition 4 makes this more rigorous. It states that a ratio of two quantities exists, when there is a multiple of each that exceeds the other. In modern notation, a ratio exists between quantities p and q, if there exist integers m and n such that mp>q and nq>p. This condition is known as the Archimedes property.

Definition 5 is the most complex and difficult. It defines what it means for two ratios to be equal. Today, this can be done by simply stating that ratios are equal when the quotients of the terms are equal, but such a definition would have been meaningless to Euclid. In modern notation, Euclid's definition of equality is that given quantities p, q, r and s, p∶q∷r ∶s if and only if, for any positive integers m and n, np<mq, np=mq, or np>mq according as nr<ms, nr=ms, or nr>ms, respectively.[19] This definition has affinities with Dedekind cuts as, with n and q both positive, np stands to mq as p/q stands to the rational number m/n (dividing both terms by nq).[20]

Definition 6 says that quantities that have the same ratio are proportional or in proportion. Euclid uses the Greek ἀναλόγον (analogon), this has the same root as λόγος and is related to the English word "analog".

Definition 7 defines what it means for one ratio to be less than or greater than another and is based on the ideas present in definition 5. In modern notation it says that given quantities p, q, r and s, p∶q>r∶s if there are positive integers m and n so that np>mq and nr≤ms.

As with definition 3, definition 8 is regarded by some as being a later insertion by Euclid's editors. It defines three terms p, q and r to be in proportion when p∶q∷q∶r. This is extended to 4 terms p, q, r and s as p∶q∷q∶r∷r∶s, and so on. Sequences that have the property that the ratios of consecutive terms are equal are called geometric progressions. Definitions 9 and 10 apply this, saying that if p, q and r are in proportion then p∶r is the duplicate ratio of p∶q and if p, q, r and s are in proportion then p∶s is the triplicate ratio of p∶q.
Number of terms and use of fractionsEdit

In general, a comparison of the quantities of a two-entity ratio can be expressed as a fraction derived from the ratio. For example, in a ratio of 2∶3, the amount, size, volume, or quantity of the first entity is {\displaystyle {\tfrac {2}{3}}}￼ that of the second entity.

If there are 2 oranges and 3 apples, the ratio of oranges to apples is 2∶3, and the ratio of oranges to the total number of pieces of fruit is 2∶5. These ratios can also be expressed in fraction form: there are 2/3 as many oranges as apples, and 2/5 of the pieces of fruit are oranges. If orange juice concentrate is to be diluted with water in the ratio 1∶4, then one part of concentrate is mixed with four parts of water, giving five parts total; the amount of orange juice concentrate is 1/4 the amount of water, while the amount of orange juice concentrate is 1/5 of the total liquid. In both ratios and fractions, it is important to be clear what is being compared to what, and beginners often make mistakes for this reason.

Fractions can also be inferred from ratios with more than two entities; however, a ratio with more than two entities cannot be completely converted into a single fraction, because a fraction can only compare two quantities. A separate fraction can be used to compare the quantities of any two of the entities covered by the ratio: for example, from a ratio of 2∶3∶7 we can infer that the quantity of the second entity is {\displaystyle {\tfrac {3}{7}}}￼ that of the third entity.
Proportions and percentage ratiosEdit

If we multiply all quantities involved in a ratio by the same number, the ratio remains valid. For example, a ratio of 3∶2 is the same as 12∶8. It is usual either to reduce terms to the lowest common denominator, or to express them in parts per hundred (percent).

If a mixture contains substances A, B, C and D in the ratio 5∶9∶4∶2 then there are 5 parts of A for every 9 parts of B, 4 parts of C and 2 parts of D. As 5+9+4+2=20, the total mixture contains 5/20 of A (5 parts out of 20), 9/20 of B, 4/20 of C, and 2/20 of D. If we divide all numbers by the total and multiply by 100, we have converted to percentages: 25% A, 45% B, 20% C, and 10% D (equivalent to writing the ratio as 25∶45∶20∶10).

If the two or more ratio quantities encompass all of the quantities in a particular situation, it is said that "the whole" contains the sum of the parts: for example, a fruit basket containing two apples and three oranges and no other fruit is made up of two parts apples and three parts oranges. In this case, {\displaystyle {\tfrac {2}{5}}}￼, or 40% of the whole is apples and {\displaystyle {\tfrac {3}{5}}}￼, or 60% of the whole is oranges. This comparison of a specific quantity to "the whole" is called a proportion.

If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4∶3 aspect ratio, which means that the width is 4/3 of the height (this can also be expressed as 1.33∶1 or just 1.33 rounded to two decimal places). More recent widescreen TVs have a 16∶9 aspect ratio, or 1.78 rounded to two decimal places. One of the popular widescreen movie formats is 2.35∶1 or simply 2.35. Representing ratios as decimal fractions simplifies their comparison. When comparing 1.33, 1.78 and 2.35, it is obvious which format offers wider image. Such a comparison works only when values being compared are consistent, like always expressing width in relation to height



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