- AThe Elements
- BThe Principia
- CArithmetica
- DThe Almagest
Step-by-Step Solution
Euclid's 'The Elements' (around 300 BCE) presented geometry as a logical system built from axioms and postulates.
Answer: A) The Elements
In which famous 13-book work did Euclid organise geometry into a deductive system?
Class 9Introduction to Euclid's GeometryGeometry — Foundations
Key idea: Euclid's axioms (common notions)
Axioms apply to all of mathematics, not just geometry. The key ones:
1. Things equal to the same thing are equal to one another. (If a = c and b = c, then a = b.)
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
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 halves of the same things are equal to one another.
These feel obvious — that's the point. Euclid wanted his foundation to be impossible to argue with.
1. Things equal to the same thing are equal to one another. (If a = c and b = c, then a = b.)
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
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 halves of the same things are equal to one another.
These feel obvious — that's the point. Euclid wanted his foundation to be impossible to argue with.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Introduction to Euclid's Geometry practice questions
More Class 9 Introduction to Euclid's Geometry practice
Euclid's fourth postulate states that ____.The equivalent of Euclid's fifth postulate that says 'through a point not on a given…Which of Euclid's common notions states 'The whole is greater than the part'?If x + 10 = 25, then x = 15 because equals were subtracted from equals. Which axiom is…Point M is the midpoint of segment PQ. If PQ = 18 cm, find PM (in cm).