NATURAL NUMBERS AND WHOLE NUMBERS

Sets of Numbers: Natural, Whole, Integers, Rational Numbers, Irrational Numbers, Real Numbers, Complex Numbers Interval Notation Set Builder Notation Number Lines, open circles, closed circles Sets and Subsets - Union and Intersection Parts of the Cartesian Plane: origin, quadrants, signs on numbers in each quadrant, x-axis, y-axis Points being symmetric to each other about the x-axis, y-axis and origin Distance Formula-calculating distance between 2 given points Midpoint-calculating midpoint between 2 given points

Are you feeling adventurous? Then spread your wings and travel km southeast of Taiwan, where you'll discover a part of the country unlike any other. Known as Lanyu* or Orchid Island, this tiny drop of earth in the Pacific* is home to the Tao*, Taiwan's only ocean-dependent indigenous* tribe. The Tao people are the people of the "alibangbang*," or flying fish, one of Mother Nature's greatest gifts. The annual flying fish season is at the heart of Tao culture and comes with many traditions and taboos. Spanning around eight months of the year, the flying fish season involves multiple customs and rituals. A special religious ceremony, usually held in February, marks the beginning of this important period and ensures a prosperous and plentiful season. Tao boat captains head to the beach with elaborate costumes on. There, they pray and make sacrifices to appeal to the flying fish spirits to bless their tribe, and to the gods for good fortune and courage on the dangerous seas. Although local fishers can catch flying fish between March and June, they are restricted to capturing only those found in shallow waters. During this period, netting* any deep-sea or coral reef fish is not permitted. If the fishers didn't follow this rule, various species would not have the time needed to recover their numbers, and harmony with nature would be lost. At the end of June, the annual sea harvest concludes with another ceremony to express gratitude and respect for nature's endless* cycles. After the ceremony, flying fish can no longer be caught. Therefore, from July onward*, only dried and stored alibangbang can be eaten. Furthermore, after the Mid-Autumn Festival*, even these dried fish must no longer be consumed. This custom seems to have been engraved in the locals’ hearts* and is believed to prevent ill luck and guarantee abundance in seasons to come. Just as the locals are concluding their scaly* harvest for the year, scores of tourists begin arriving on Lanyu for the summer season. To make sure you don't feel like a fish out of water, here are some basic guidelines to help you enjoy your stay while respecting local traditions. First, it is considered a taboo to touch or photograph the Tao fishing boats without permission since it would bring bad luck. Also, you should never enter locals’ private gardens uninvited* to view or sample drying fish. Additionally, avoid asking about future fishing trips, as locals believe that the gods may be angered and that the harvest may be spoiled as a consequence. Finally, as a sign of respect for the local community and environment, don't snorkel* or dive in the island's traditional fishing waters during the flying fish season. Such activities can disturb the local ecosystem. The customs and taboos mentioned above reflect the importance of preserving and cherishing natural resources and local culture. The ancient wisdom of Lanyu’s Tao inhabitants thus appears to give us much to learn about living in harmony with this planet. Everyone is, after all, in the same boat under nature's wing.

Alright, Isti — here’s a longer and more detailed English version of the Isaac Newton text, still written at a level that’s accessible for Grade 4 students, but rich enough in information to meet PISA literacy expectations and EF A2-level vocabulary. I’ve kept sentences short, clear, and with explanations for new concepts so it’s easier for young learners to follow, while still including both famous facts and lesser-known stories. ⸻ Isaac Newton: The Man Who Changed the Way We See the World A Boy from a Small Village Isaac Newton was born on January 4, 1643, in Woolsthorpe, a small village in England. His life was not easy. His father died before he was born. When he was just a few months old, his mother remarried and left him to live with his grandmother. Isaac missed his parents, but he kept himself busy by making things and exploring the world around him. As a child, Isaac liked to build models and machines. He made a small windmill that could turn with the wind. He built a water clock that told the time by dripping water into a container. He even made a sundial — a clock that tells the time by using the shadow of the sun. 💡 Did you know? The sundial marks that Isaac carved as a boy can still be seen today on the wall of his old house. ⸻ School and Curiosity When Newton first went to school, he was not the top student. At first, he did not pay much attention in class. But one day, another boy teased him for not being smart. Newton decided to study hard to prove him wrong. Soon, he became the best in his class. Isaac loved asking questions. He wanted to know how and why things happened. He enjoyed watching the stars at night and thinking about how the world worked. ⸻ The Falling Apple and Gravity One of the most famous stories about Newton is the falling apple. One afternoon, Isaac sat in his mother’s garden and saw an apple drop from a tree. This made him think: “Why does the apple fall straight down? Why doesn’t it fly up into the sky?” From this question, Newton began to think about gravity — an invisible force that pulls objects toward each other. Gravity is what keeps our feet on the ground. It’s also what keeps the Moon moving around the Earth and the planets moving around the Sun. 💡 Fun fact: The apple did not hit Newton’s head. That’s just a story people made up later to make the tale more exciting. ⸻ Newton’s Three Laws of Motion Newton studied movement and wrote three important rules: 1. Objects stay still or keep moving unless something makes them change. • Example: A ball will not roll unless you push it. 2. The bigger the push, the bigger the movement. • Example: If you kick a ball harder, it will go faster and farther. 3. Every action has an equal and opposite reaction. • Example: When you jump off a boat, the boat moves backward as you move forward. These three laws are still used today to understand how cars, rockets, and even roller coasters work. ⸻ Discoveries in Light and Color Newton also studied light. He found that white light is not just one color — it is made of many colors. He used a glass prism to split sunlight into a rainbow. This helped scientists understand how colors work. ⸻ Inventions and New Ideas Newton made a special telescope that used mirrors instead of lenses. This type of telescope made images of planets and stars much clearer. It is still called the Newtonian telescope today. He also worked in mathematics and helped create a new type of math called calculus, which is used to study changes and movement. ⸻ Strange Experiments Newton was so curious that he sometimes tested ideas on himself. Once, he put a thin needle, called a bodkin, beside his eye to see how it would change his vision. It was very dangerous, but luckily he did not go blind. 💡 Did you know? Newton also studied alchemy — an old kind of science where people tried to turn metal into gold. He never succeeded, but it showed how wide his interests were. ⸻ Later Life and Work At the age of 27, Newton became a professor at Cambridge University. He later worked for the Royal Mint, making sure coins were made safely and stopping people from making fake money. He was very strict, and some criminals were sent to prison because of his work. Newton never married. He spent most of his life reading, writing, and doing experiments. ⸻ The End of His Life Isaac Newton died in 1727 at the age of 84. He was buried in Westminster Abbey, a famous place in London where great people of Britain are honored. His work changed the world forever. Even today, scientists, engineers, and students still use Newton’s laws and ideas. 💬 Newton once said: “If I have seen further, it is by standing on the shoulders of giants.” This means we can make new discoveries by learning from the work of others who came before us. give 10 questions to each passage with PISA literacy standard for kid 10 years, 1. Nikola Tesla: The Man Who Dreamed of Lightning Born: July 10, 1856 Died: January 7, 1943 When Nikola Tesla was a boy in Croatia, he saw a flash of lightning and asked his mother, “Can we catch the light?” That question never left him. As he grew older, Tesla became a brilliant inventor, especially fascinated by electricity. He believed in a future where energy could be sent wirelessly through the air—like music through the radio! Tesla invented the alternating current (AC) system, which became the foundation of modern electricity. At the time, Thomas Edison promoted direct current (DC), and the two men had a fierce competition. Many laughed at Tesla's bold ideas, but he never gave up. He dreamed of wireless communication, flying machines, and even free energy for everyone. Though he died alone and poor, today the world honors his vision. Think About It: Why do you think people didn’t believe Tesla at first? What can we learn from Tesla’s courage to dream big? 2. Charles Darwin: The Man Who Studied the World’s Weirdest Creatures Born: February 12, 1809 Died: April 19, 1882 When young Charles Darwin got on a ship called HMS Beagle, he didn’t know he would change science forever. He sailed around the world for five years, collecting plants, animals, and fossils. On the Galápagos Islands, he noticed something curious: finches had different beaks depending on their island. Why? Darwin’s observations led him to write the theory of evolution by natural selection. It explained how animals adapt and survive. But his ideas shocked many people because they seemed to challenge religious beliefs. Despite the controversy, Darwin continued his work. His book On the Origin of Species changed how we see life on Earth. Think About It: Should scientists share their ideas even if they go against what others believe? How did traveling help Darwin make new discoveries? 3. Marie Curie: The Woman Who Glowed in the Dark Born: November 7, 1867 Died: July 4, 1934 Marie Curie was born in Poland at a time when girls were not allowed to study science. But that didn’t stop her. She moved to France, worked day and night, and discovered radioactivity, a powerful energy hidden inside atoms. She and her husband, Pierre Curie, found two new elements: polonium and radium. She became the first woman to win a Nobel Prize, and the only person to win in two different sciences: physics and chemistry. Even when Pierre died in an accident, Marie continued their work. Her discoveries helped doctors treat cancer—but working with radioactive materials also harmed her health. She died from radiation exposure, but her legacy lives on. Think About It: What challenges did Marie Curie face as a woman in science? Why is it important to balance discovery with safety? 4. Galileo Galilei: The Star Watcher Who Defied the Church Born: February 15, 1564 Died: January 8, 1642 Galileo loved looking at the stars. He built one of the first powerful telescopes and made stunning discoveries: mountains on the Moon, moons around Jupiter, and that the Earth orbits the Sun—not the other way around. This idea, called heliocentrism, went against the teachings of the Church. He was put on trial and forced to say he was wrong. But he wasn’t. He spent his last years under house arrest, quietly writing. Today, Galileo is called the father of modern science for daring to question what others blindly believed. Think About It: Why do you think Galileo was punished for telling the truth? Should science always follow evidence, even if it goes against powerful beliefs? 5. Isaac Newton: The Man Who Asked “Why?” When an Apple Fell Born: January 4, 1643 Died: March 31, 1727 One day, an apple fell from a tree, and Isaac Newton began to wonder: Why did it fall down, not sideways or up? This simple question led to his theory of gravity. Newton also invented calculus, described the laws of motion, and changed physics forever. But Newton wasn’t just a genius—he was curious, quiet, and often worked alone. He believed everything in nature followed rules, and it was our job to discover them. Thanks to him, we understand how planets move, how rockets launch, and why you fall when you trip. Think About It: How did Newton’s curiosity lead to great discoveries? Do you think working alone helped or hurt Newton? 6. Ada Lovelace: The First Computer Programmer Before Computers Existed Born: December 10, 1815 Died: November 27, 1852 Ada Lovelace was the daughter of the famous poet Lord Byron, but she didn’t love poetry—she loved numbers! At a time when girls were expected to sew, Ada studied mathematics. She met Charles Babbage, who designed an early computer called the Analytical Engine. Ada imagined the machine could do more than just math—it could create music, art, and even write! She wrote what is now considered the first computer program, long before real computers were built. Think About It: How did Ada imagine something that didn’t exist yet? Why do we call her a pioneer in technology? 7. Albert Einstein: The Man Who Brought Time and Space Together Born: March 14, 1879 Died: April 18, 1955 Albert Einstein wasn’t always a good student. In fact, his teachers thought he was slow. But Einstein thought deeply. He asked big questions like, “What if you could ride a beam of light?” His theories of relativity changed how we see space, time, and gravity. He also warned the world about the dangers of nuclear weapons, even though his ideas helped create them. Einstein believed science should help people, not harm them. With his messy hair, kind smile, and brilliant mind, he remains a symbol of genius. Think About It: Can someone be bad in school but still be brilliant? Should scientists be responsible for how their inventions are used? 8. Pythagoras: The Musician Who Loved Math Born: Around 570 BC Died: Around 495 BC Long ago in ancient Greece, Pythagoras believed the universe followed numbers. He discovered the Pythagorean Theorem, a rule about triangles that helps us build houses, design computers, and navigate space. He also believed that music had math inside it—that certain notes made perfect harmony because of mathematical ratios. Pythagoras started a secret school and taught his students to search for truth through numbers, shapes, and sound. Think About It: Why do you think Pythagoras saw math in everything? How does music relate to math? 9. Rosalind Franklin: The Woman Behind the DNA Discovery Born: July 25, 1920 Died: April 16, 1958 Rosalind Franklin loved looking closely at things. She used a special machine called X-ray crystallography to photograph molecules. One of her greatest photos, called Photo 51, showed the shape of DNA, the molecule that carries life’s instructions. But her work was taken without credit. Two men, Watson and Crick, used her photo to build their famous model of DNA and won the Nobel Prize. Rosalind died young and never knew how important her work became. Think About It: Why is it important to give credit in science? What can we learn from Rosalind’s quiet strength? 10. Carl Linnaeus: The Man Who Gave Names to Everything Born: May 23, 1707 Died: January 10, 1778 Have you ever wondered why a tiger is called Panthera tigris? That’s thanks to Carl Linnaeus, a Swedish scientist who created a way to name and organize every living thing. His system is still used today in biology. Linnaeus loved nature and spent his life collecting plants, animals, and even rocks. He believed that by organizing life, we could better understand it. Thanks to him, we now have a global “dictionary of nature.” Think About It: Why is it important to name and organize living things? How does order help us understand the world?

Soils Southeast Asia, on balance, has a higher proportion of relatively fertile soils than most tropical regions, and soil erosion is less severe than elsewhere. Much of the region, however, is covered by tropical soils that generally are quite poor in nutrients. Often the profusion of plant life is more related to heat and moisture than to soil quality, even though these climatic conditions intensify both chemical weathering and the rate of bacterial action that usually improve soil fertility. Once the vegetation cover is removed, the supply of humus quickly disappears. In addition, the often heavy rainfall leaches the soils of their soluble nutrients, hastens erosion, and damages the soil texture. The leaching process in part results in laterites of reddish clay that contain hydroxides of iron and alumina. Laterite soils are common in parts of Myanmar, Thailand, and Vietnam and also occur in the islands of the Sunda Shelf, notably Borneo. The most fertile soils occur in regions of volcanic activity, where the ejecta is chemically alkaline or neutral. Such soils are found in parts of Sumatra and much of Java in Indonesia. The alluvial soils of the river valleys also are highly fertile and are intensively cultivated. Climate All of Southeast Asia falls within the warm, humid tropics, and its climate generally can be characterized as monsoonal (i.e., marked by wet and dry periods). Changing seasons are more associated with rainfall than with temperature variations. There is, however, a high degree of climatic complexity within the region. Temperatures Regional temperatures at or near sea level remain fairly constant throughout the year, although monthly averages tend to vary more with increasing latitude. Thus, with the exception of northern Vietnam, annual average temperatures are close to 80 °F (27 °C). Increasing elevation acts to decrease average temperatures, and such locations as the Cameron Highlands in peninsular Malaysia and Baguio in the Philippines have become popular tourist destinations in part because of their relatively cooler climates. Proximity to the sea also tends to moderate temperatures. Precipitation Much of Southeast Asia receives more than 60 inches (1,500 millimeters) of rainfall annually, and many areas commonly receive double and even triple that amount. The rainfall pattern is distinctly affected by two prevailing air currents: the northeast (or dry) monsoon and the southwest (or wet) monsoon. The northeast monsoon occurs roughly from November to March and brings relatively dry, cool air and little precipitation to the mainland. As the southwestward-flowing air passes over the warmer sea, it gradually warms and gathers moisture. Precipitation is especially heavy where the airstream is forced to rise over mountains or encounters a landmass. The east coast of peninsular Malaysia, the Philippines, and parts of eastern Indonesia receive the heaviest rains during this period. The southwest monsoon prevails from May to September, when the air current reverses and the dominant flow is to the northeast. The mainland receives the bulk of its rainfall during this period. Over much of the southern Malay Peninsula and insular Southeast Asia there is little or no prolonged dry season. This is especially marked in much of the equatorial region and along the east coast of the Philippines. While the dry and wet monsoons are important in explaining rainfall patterns, so too are such factors as relief, land and sea breezes, convectional overturning and cyclonic disturbances. These factors often are combined with monsoonal effects to produce highly variable rainfall patterns over relatively short distances. While many of the cyclonic disturbances produce only moderate rainfall, others mature into tropical storms—called cyclones in the Indian Ocean and typhoons in the Pacific—that bring heavy rains and destruction to the areas over which they pass. The Philippines are particularly affected by these storms. Plant life Tropical forests in Southeast Asia Tropical forests in Southeast Asia The seasonal nature and pattern of Southeast Asia’s rainfall, as well as the region’s physiography, have strongly affected the development of natural vegetation. The hot, humid climate and enormous variety of habitats have given rise to an abundance and diversity of vegetative forms unlike that in any other area of the world. Much of the natural vegetation has been modified by human action, although large areas of relatively untouched land still can be found. The vegetation can be grouped into two broad categories: the tropical-evergreen forests of the equatorial lowlands and the open type of tropical-deciduous, or “monsoon,” forests in areas of seasonal drought. The evergreen forests are characterized by multiple stories of vegetation, consisting of a variety of trees and plants. Although a large diversity of tree species is found in these forests, members of the Dipterocarpaceae family account for roughly half of the varieties. Deciduous forests are found in eastern Indonesia and those parts of the mainland where annual rainfall does not exceed 80 inches. Just as in the equatorial forest, a wide variety of species is normally the rule. Certain species, such as teak, have become highly valued commercially. Teak is found in parts of Indonesia, Myanmar, Thailand, and Laos. In addition to these two basic types of vegetation, other regional patterns reflect topography. Especially noteworthy are coastal and highland plant communities. Mangrove belts, of which there are more than 30 varieties, occur where silt is deposited in coastal areas. Upland forests dominated by maples, oaks, and magnolias are found especially on mainland mountain slopes. Human activity has been rapidly altering the stands of virgin forest in Southeast Asia. Most deforestation results from removal for fuelwood and clearing for agriculture and grazing. Although only a relatively small portion of the total land area has been permanently cleared for cultivation—e.g., in Java (Indonesia) and western Luzon (the Philippines)—in some areas shifting cultivation has brought about the replacement of virgin forest with secondary growth. In addition, nearly all countries have commercial logging industries; notable are those in Indonesia, Malaysia, Thailand, and Myanmar. A growing problem has been illegal logging. Thus, timber harvesting has come to contribute significantly to deforestation. Programs in social forestry and reforestation have yet to halt the rapid denuding of the landscape. Animal life Southeast Asia is situated where two major divisions of the world’s fauna meet. The region itself constitutes the eastern half of what is called the Oriental, or Indian, zoogeographic region (part of the much larger realm of Megagaea). Bordering along the south and east is the Australian zoogeographic region, and the eastern portion of insular Southeast Asia—Celebes (Sulawesi), the Moluccas, and the Lesser Sunda Islands—constitutes a transition zone between these two faunal regions. a classroom in Brazil More From Britannica education: Southeast Asia Southeast Asia is notable, therefore, for a considerable diversity of wildlife throughout the region. These differences are especially striking between the species of the eastern and western fringes as well as between those of the archipelagic south and the mainland north. The differences stem largely from the isolation, over varying lengths of geologic time, of species following their migration from the Asian continent. In addition, the tropical rain forests in many parts of the region, with their great diversity of vegetation, have made possible the development of complex communities of animals that fill specialized ecological niches. Especially numerous are arboreal and flying creatures. orangutans orangutansOrangutans (Pongo pygmaeus) in Sumatra, Indonesia. The distinction between the two faunal regions is best depicted by their mammal populations. In general, Australia is inhabited largely by marsupials (pouched mammals) and monotremes (egg-laying mammals), while Southeast Asia contains placental mammals and such hybrid species as the bandicoot of eastern Indonesia. Small mammals such as monkeys and shrews are the most numerous, while in many areas the larger mammals have been pushed into more remote areas and national preserves. Bears, gibbons, elephants, deer, civets, and pigs are found in both mainland and insular Southeast Asia, as are diminishing numbers of tigers. The Malayan tapir, a relative of the rhinoceros, is native to the Malay Peninsula and Sumatra, while the tarsier is found in the Philippines and parts of Indonesia. A number of rare endemic species are found in Indonesia and East (insular) Malaysia, including the Sumatran and Javan rhinoceros, the orangutan, the anoa (a dwarf buffalo), the babirusa (a wild swine), and the palm civet. As the pace of development accelerates and populations continue to expand in Southeast Asia, concern has increased regarding the impact of human activity on the region’s environment. A significant portion of Southeast Asia, however, has not changed greatly and remains an unaltered home to wildlife. The nations of the region, with only few exceptions, have become aware of the need to maintain forest cover not only to prevent soil erosion but to preserve the diversity of flora and fauna. Indonesia, for example, has created an extensive system of national parks and preserves for this purpose. Even so, such species as the Javan rhinoceros face extinction, with only a handful of the animals remaining in western Java

Fed. 51: To the People of the State of New York: TO WHAT expedient, then, shall we finally resort, for maintaining in practice the necessary partition of power among the several departments, as laid down in the Constitution? The only answer that can be given is, that as all these exterior provisions are found to be inadequate, the defect must be supplied, by so contriving the interior structure of the government as that its several constituent parts may, by their mutual relations, be the means of keeping each other in their proper places. Without presuming to undertake a full development of this important idea, I will hazard a few general observations, which may perhaps place it in a clearer light, and enable us to form a more correct judgment of the principles and structure of the government planned by the convention. In order to lay a due foundation for that separate and distinct exercise of the different powers of government, which to a certain extent is admitted on all hands to be essential to the preservation of liberty, it is evident that each department should have a will of its own; and consequently should be so constituted that the members of each should have as little agency as possible in the appointment of the members of the others. Were this principle rigorously adhered to, it would require that all the appointments for the supreme executive, legislative, and judiciary magistracies should be drawn from the same fountain of authority, the people, through channels having no communication whatever with one another. Perhaps such a plan of constructing the several departments would be less difficult in practice than it may in contemplation appear. Some difficulties, however, and some additional expense would attend the execution of it. Some deviations, therefore, from the principle must be admitted. In the constitution of the judiciary department in particular, it might be inexpedient to insist rigorously on the principle: first, because peculiar qualifications being essential in the members, the primary consideration ought to be to select that mode of choice which best secures these qualifications; secondly, because the permanent tenure by which the appointments are held in that department, must soon destroy all sense of dependence on the authority conferring them. It is equally evident, that the members of each department should be as little dependent as possible on those of the others, for the emoluments annexed to their offices. Were the executive magistrate, or the judges, not independent of the legislature in this particular, their independence in every other would be merely nominal. But the great security against a gradual concentration of the several powers in the same department, consists in giving to those who administer each department the necessary constitutional means and personal motives to resist encroachments of the others. The provision for defense must in this, as in all other cases, be made commensurate to the danger of attack. Ambition must be made to counteract ambition. The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions. This policy of supplying, by opposite and rival interests, the defect of better motives, might be traced through the whole system of human affairs, private as well as public. We see it particularly displayed in all the subordinate distributions of power, where the constant aim is to divide and arrange the several offices in such a manner as that each may be a check on the other that the private interest of every individual may be a sentinel over the public rights. These inventions of prudence cannot be less requisite in the distribution of the supreme powers of the State. But it is not possible to give to each department an equal power of self-defense. In republican government, the legislative authority necessarily predominates. The remedy for this inconveniency is to divide the legislature into different branches; and to render them, by different modes of election and different principles of action, as little connected with each other as the nature of their common functions and their common dependence on the society will admit. It may even be necessary to guard against dangerous encroachments by still further precautions. As the weight of the legislative authority requires that it should be thus divided, the weakness of the executive may require, on the other hand, that it should be fortified. An absolute negative on the legislature appears, at first view, to be the natural defense with which the executive magistrate should be armed. But perhaps it would be neither altogether safe nor alone sufficient. On ordinary occasions it might not be exerted with the requisite firmness, and on extraordinary occasions it might be perfidiously abused. May not this defect of an absolute negative be supplied by some qualified connection between this weaker department and the weaker branch of the stronger department, by which the latter may be led to support the constitutional rights of the former, without being too much detached from the rights of its own department? If the principles on which these observations are founded be just, as I persuade myself they are, and they be applied as a criterion to the several State constitutions, and to the federal Constitution it will be found that if the latter does not perfectly correspond with them, the former are infinitely less able to bear such a test. There are, moreover, two considerations particularly applicable to the federal system of America, which place that system in a very interesting point of view. First. In a single republic, all the power surrendered by the people is submitted to the administration of a single government; and the usurpations are guarded against by a division of the government into distinct and separate departments. In the compound republic of America, the power surrendered by the people is first divided between two distinct governments, and then the portion allotted to each subdivided among distinct and separate departments. Hence a double security arises to the rights of the people. The different governments will control each other, at the same time that each will be controlled by itself. Second. It is of great importance in a republic not only to guard the society against the oppression of its rulers, but to guard one part of the society against the injustice of the other part. Different interests necessarily exist in different classes of citizens. If a majority be united by a common interest, the rights of the minority will be insecure. There are but two methods of providing against this evil: the one by creating a will in the community independent of the majority that is, of the society itself; the other, by comprehending in the society so many separate descriptions of citizens as will render an unjust combination of a majority of the whole very improbable, if not impracticable. The first method prevails in all governments possessing an hereditary or self-appointed authority. This, at best, is but a precarious security; because a power independent of the society may as well espouse the unjust views of the major, as the rightful interests of the minor party, and may possibly be turned against both parties. The second method will be exemplified in the federal republic of the United States. Whilst all authority in it will be derived from and dependent on the society, the society itself will be broken into so many parts, interests, and classes of citizens, that the rights of individuals, or of the minority, will be in little danger from interested combinations of the majority. In a free government the security for civil rights must be the same as that for religious rights. It consists in the one case in the multiplicity of interests, and in the other in the multiplicity of sects. The degree of security in both cases will depend on the number of interests and sects; and this may be presumed to depend on the extent of country and number of people comprehended under the same government. This view of the subject must particularly recommend a proper federal system to all the sincere and considerate friends of republican government, since it shows that in exact proportion as the territory of the Union may be formed into more circumscribed Confederacies, or States oppressive combinations of a majority will be facilitated: the best security, under the republican forms, for the rights of every class of citizens, will be diminished: and consequently the stability and independence of some member of the government, the only other security, must be proportionately increased. Justice is the end of government. It is the end of civil society. It ever has been and ever will be pursued until it be obtained, or until liberty be lost in the pursuit. In a society under the forms of which the stronger faction can readily unite and oppress the weaker, anarchy may as truly be said to reign as in a state of nature, where the weaker individual is not secured against the violence of the stronger; and as, in the latter state, even the stronger individuals are prompted, by the uncertainty of their condition, to submit to a government which may protect the weak as well as themselves; so, in the former state, will the more powerful factions or parties be gradnally induced, by a like motive, to wish for a government which will protect all parties, the weaker as well as the more powerful. It can be little doubted that if the State of Rhode Island was separated from the Confederacy and left to itself, the insecurity of rights under the popular form of government within such narrow limits would be displayed by such reiterated oppressions of factious majorities that some power altogether independent of the people would soon be called for by the voice of the very factions whose misrule had proved the necessity of it. In the extended republic of the United States, and among the great variety of interests, parties, and sects which it embraces, a coalition of a majority of the whole society could seldom take place on any other principles than those of justice and the general good; whilst there being thus less danger to a minor from the will of a major party, there must be less pretext, also, to provide for the security of the former, by introducing into the government a will not dependent on the latter, or, in other words, a will independent of the society itself. It is no less certain than it is important, notwithstanding the contrary opinions which have been entertained, that the larger the society, provided it lie within a practical sphere, the more duly capable it will be of self-government. And happily for the REPUBLICAN CAUSE, the practicable sphere may be carried to a very great extent, by a judicious modification and mixture of the FEDERAL PRINCIPLE. PUBLIUS.

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