This version is given by Sir Thomas Heath (1861-1940) in The Elements of Euclid. (1908)

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Axioms

Things which are equal to the same thing are also equal to one another.
If equals be added to equals, the wholes are equal.
If equals be subtracted from equals, the remainders are equal.
Things which coincide with one another are equal to one another.
The whole is greater than the part.

Postulates

To draw a straight line from any point to any point.
To produce a finite straight line continuously in a straight line.
To describe a circle with any center and distance.
That all right angles are equal to one another.
That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less that two right angles.*‍

In 1795, John Playfair (1748-1819) proposed an alternative version of the Fifth Postulate, which leads to the same geometry as Euclid's.

It is Playfair's rendition of the Fifth Postulate that frequently emerges in discussions of Euclidean Geometry.

5'.Through a given point P not on a line L, there is one and only one line in the plane of P and L which does not meet L.

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Problems

Challenging Triangle Congruence

Properties of a Right-Angled Triangle

Circumcircle of a Triangle

Inscribed Quadrilateral

Geometry Warm-Up: Angles and Lines

Axioms and Postulates of Euclid

Morley's Triangle

Minimum and Maximum Problems in Geometry

Where do you hold your classes?

We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.

What do you need to start learning online?

For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.

When can I take the trial lesson?

You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.

What should I expect from the trial lesson?

The trial lesson is a 30-minute online session designed to get a sense of how your child approaches mathematical thinking and problem solving. (In practice, it often runs a bit longer if the student is engaged!)

We typically explore a range of fun and challenging problems drawn from competitions. We adapt the difficulty based on how the student responds, aiming to make it both accessible and stimulating.

After the session, we’ll have a quick conversation with the parent to share observations and suggest a personalised path forward.

I can't attend class, what should I do?

It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to

I don't have much free time, will I have time to study?

Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.

How long is one lesson?

All classes last 1 hour.

Meet our team

Our teachers will tell you how to prepare for exams, help you cope with difficult tasks and win the Olympiad
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They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them

George Ionitsa

Founder &
Maths and Coding Coach

Hear from some of our amazing students who already achieved incredible results with us!

"Olympiad Maths Lessons helped me a lot to get the Gold medal in Junior Maths Challenge"

St. Paul's Student

"Thanks to the 'Data Science' and 'Coding in Python' lessons I got accepted to my dream university."

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Warwick University

"Great courses, which thoroughly explained topics beyond the capability of the GCSE answer sheet. Thanks so much."

Ivan

GCSE Student in Dubai

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VC Investor

"We got silver in PMC! Thanks George!"

Mum of St. Paul's Student

Prepare for the Primary Maths Challenge

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Python with Turtle