1. Euclid defined axioms as common notions used throughout mathematics, while postulates were specific assumptions used in geometry.
2. The document lists Euclid's common axioms like "things equal to the same thing are equal" and postulates like "a straight line can be drawn between any two points."
3. It provides examples of theorems like two lines cannot intersect in more than one point, and exercises analyzing statements and defining terms related to geometry.
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APEX INSTITUTE has been established with sincere and positive resolve to do something rewarding for ENGG. / PRE-MEDICAL aspirants. For this the APEX INSTITUTE has been instituted to provide a relentlessly motivating and competitive atmosphere.
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How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. Axioms and Postulates
▪Euclid, starting from his definitions, assumed
certain properties, which were not to be
proved.These assumptions are actually
‘obvious universal truths’, in which he divided
into two: axioms and postulates.
3. Axioms and Postulates
▪Assumptions that were specific to Geometry
are called POSTULATES
▪Common notions or AXIOMS, on the other
hand, were assumptions used throughout
Mathematics and not specifically linked to
Geometry
4. Axioms
1. Things which are equal to the same thing
are equal to one another
2. If equals are added to equals, the wholes
are equal.
3. If equals are subtracted from equals, the
remainders are equals.
5. Axioms
4. Things which coincide with one another are
equal to one another.
5. The whole is greater than the part.
6. Things which are double of the same things are
equal to one another.
7. Things which are Half of the same things are
equal to one another.
6. Postulates
1. A straight line segment can be drawn joining
any two points
2. Any straight line can be extended indefinitely in
a straight line.
3. Given any straight line segment, a circle can be
drawn having the segment as radius and one
endpoint as center.
7. Postulates
1. A straight line segment can be drawn joining
any two points
Axiom 5.1
Given two distinct points, there is a unique line that
passes through them.
8. Postulates
4. All right angles are congruent.
5. If two lines are drawn which intersect a third in
such a way that the sum of the inner angles on
one side is less than two right angles, then the
two lines inevitably must intersect each other
on that side if extended far enough.
10. Exercise
1. Which of the following statements are true and
which are false? Give reasons for your answers.
a. Only one line can pass through a single point.
b. There are an infinite number of lines which pass
through two distinct points.
c. Any straight line can be extended indefinitely in a
straight line.
d. If two circles are equal, then their radius are equal.
11. Exercise
2. Give a definition for each of the following terms.
a. parallel lines d. radius of a circle
b. perpendicular lines e. square
c. line segment
12. Exercise
3. Consider two postulates given below:
a. Given any two distinct points A and B, there
exists a third point C which is in between A and B.
b.There exist at least three points that are not
on the same line.
Are these postulates consistent? Do they
follow Euclid’s postulates? Explain.
Editor's Notes
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?
2 & 4
8 & -2
-5 & 3
6 & -2
3 & 3
-7 & 2
How did you find the two numbers in column 4 to satisfy the conditions in columns 2 (sum) and 3(product)?
Was it easy to find the two numbers?
What does it mean when the product of the numbers is negative? positive?
Did you recognize a pattern or technique on how to find the two numbers given its sum and product? What is it?