In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

When working exclusively in two-dimensional Euclidean space, the definite article is used, so, "the" plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, or, in other words, in the plane.

Euclid set forth the first great landmark of mathematical thought, an axiomatic treatment of geometry. He selected a small core of undefined terms (called "common notions") and postulates (or axioms) which he then used to prove various geometrical statements. Although the plane in its modern sense is not directly given a definition anywhere in the "Elements", it may be thought of as part of the common notions. Euclid never used numbers to measure length, angle, or area. In this way the Euclidean plane is not quite the same as the Cartesian plane. What are the answers to this following set of questions: 1. How is a plane described in mathmatics?
2. Who set fourth the first great landmark of mathmatical thought?
3. What was it?
4. In what aspects of mathematics are performed in two-dimensional space in other words in the plane?
5. Did Euclid ever use numbers to measure length, angle or area?
6. Is that the same as a Cartesian plane?
7. How can a plane arise?
8. What article is used when working exclusivley in two-dimensionial Euclidean space?
9. Then what does the plane refer to?
10. What did Euclid use to prove various geometric statements?
Answer: 1. a plane is a flat, two-dimensional surface that extends infinitely far
2. Euclid
3. an axiomatic treatment of geometry
4. geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, or, in other words
5. No
6. no
7. as subspaces of some higher-dimensional space
8. the definite article is used
9. the whole space
10. He selected a small core of undefined terms (called "common notions") and postulates (or axioms)

Problem: Prince Edward Island (PEI or P.E.I.; ) is a province of Canada consisting of the island of the same name, as well as several much smaller islands.

Prince Edward Island is one of the three Maritime Provinces and is the smallest province in both land area and population. It is the only subnational jurisdiction of North America outside the Caribbean to have no mainland territory, and the only such jurisdiction to have no land boundary. The island has several informal names: "Garden of the Gulf," referring to the pastoral scenery and lush agricultural lands throughout the province; and "Birthplace of Confederation" or "Cradle of Confederation", referring to the Charlottetown Conference in 1864, although PEI did not join Confederation until 1873, when it became the seventh Canadian province. The backbone of the economy is farming; it produces 25% of Canada's potatoes. Historically, PEI is one of Canada's older settlements and demographically still reflects older immigration to the country, with Celtic, Anglo-Saxon and French surnames being dominant to this day.

According to the 2016 census, the province of Prince Edward Island has 142,907 residents. It is located about north of Halifax, Nova Scotia and east of Quebec City. It consists of the main island and 231 minor islands. Altogether, the entire province has a land area of . Its capital is Charlottetown.
1. How many people are there in the province of Prince Edward Island?
2. What is Prince Edward Island?
3. What is one or the informal names for it?
4. What is another?
5. What is the basis of its economy?
6. What's its third informal name?
7. How much or Canada's potatoes does it grow?
8. What kind of surnames would you find there?
9. Besides the main island, how many others does it have?
10. How many minor islands does it have?
11. What kind of Province is it?
12. What other kind of province is it one of?
13. How many Maritime Provinces are there total?
14. When was the Charlottetown Conference?
15. What happened in 1873?
16. What is it situated north of?
17. And what city is it east of?
18. What is it a subnational jurisdiction of?
19. Does it have a mainland territory?
20. Is it a newer settlement?
Answer: 1. 142,907
2. it is a province of Canada consisting of the island of the same name, as well as several much smaller islands
3. : "Garden of the Gulf,"
4. "Birthplace of Confederation"
5. The backbone of the economy is farming
6. "Cradle of Confederation"
7. 25%
8. Celtic, Anglo-Saxon and French surnames
9. several much smaller islands
10. 231 minor islands
11. a Canadian province
12. a Maritime Provinc
13. three
14. in 1864
15. it joined the Confederation
16. Halifax
17. Quebec City
18. subnational jurisdiction of North America
19. no
20. no

question: CHAPTER XL

"For once," Lady Carey said, with a faint smile, "your 'admirable Crichton' has failed you."

Lucille opened her eyes. She had been leaning back amongst the railway cushions.

"I think not," she said. "Only I blame myself that I ever trusted the Prince even so far as to give him that message. For I know very well that if Victor had received it he would have been here."

Lady Carey took up a great pile of papers and looked them carelessly through.

"I am afraid," she said, "that I do not agree with you. I do not think that Saxe Leinitzer had any desire except to see you safely away. I believe that he will be quite as disappointed as you are that your husband is not here to aid you. Some one must see you safely on the steamer at Havre. Perhaps he will come himself."

"I shall wait in Paris," Lucille said quietly, "for my husband."

"You may wait," Lady Carey said, "for a very long time."

Lucille looked at her steadily. "What do you mean?"

"What a fool you are, Lucille. If to other people it seems almost certain on the face of it that you were responsible for that drop of poison in your husband's liqueur glass, why should it not seem so to himself?"

Lucille laughed, but there was a look of horror in her dark eyes.

"How absurd. I know Victor better than to believe him capable of such a suspicion. Just as he knows me better than to believe me capable of such an act."
1. Who was to wait in Paris?
2. Why?
3. and his name?
4. and who was she discussing this with?
5. Did she think it was a good idea?
6. Why not?
7. Who does she have distrust now for?
****
answer:
1. Lucille
2. for her husband
3. Victor
4. Lady Carey
5. No
6. blame for poisoning him
7. I know Victor better than to believe him capable of such a suspicion., Victor