Euclid

Father of geometry

Ancient influential 90 sayings

Sayings by Euclid

Things which are equal to the same thing are also equal to one another.

c. 300 BCE — Common Notion 1, from 'Elements'

Strange & Unusual Confirmed

A figure is that which is contained by any boundary or boundaries.

c. 300 BCE — Definition 14, Book I of 'Elements'

Strange & Unusual Confirmed

A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another.

c. 300 BCE — Definition 15, Book I of 'Elements'

Strange & Unusual Confirmed

In any right-angled triangle, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

c. 300 BCE — Theorem 47 (Pythagorean Theorem), Book I of 'Elements'

Strange & Unusual Unverifiable

If a straight line be cut into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts together with the square on the line between the points of section is equal to the square on the half.

c. 300 BCE — Theorem 5, Book II of 'Elements'

Strange & Unusual Unverifiable

The angles in the same segment are equal to one another.

c. 300 BCE — Theorem 21, Book III of 'Elements'

Strange & Unusual Unverifiable

If a straight line touch a circle, and from the point of contact there be drawn across in the circle a straight line cutting the circle, the angles which it makes with the tangent will be equal to the angles in the alternate segments of the circle.

c. 300 BCE — Theorem 32, Book III of 'Elements'

Strange & Unusual Unverifiable

To construct an equilateral triangle on a given finite straight line.

c. 300 BCE — Proposition 1, Book I of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

To cut off from the greater of two given unequal straight lines a straight line equal to the less.

c. 300 BCE — Proposition 3, Book I of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend.

c. 300 BCE — Proposition 4 (Side-Angle-Side Congruence), Book I of 'Elements'

Strange & Unusual Unverifiable

In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another.

c. 300 BCE — Proposition 5 (Pons Asinorum), Book I of 'Elements'

Strange & Unusual Unverifiable

To bisect a given rectilinear angle.

c. 300 BCE — Proposition 9, Book I of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

To draw a straight line at right angles to a given straight line from a given point on it.

c. 300 BCE — Proposition 11, Book I of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles.

c. 300 BCE — Proposition 29, Book I of 'Elements'

Strange & Unusual Unverifiable

In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.

c. 300 BCE — Proposition 32, Book I of 'Elements'

Strange & Unusual Unverifiable

Parallelograms which are on the same base and in the same parallels are equal to one another.

c. 300 BCE — Proposition 35, Book I of 'Elements'

Strange & Unusual Unverifiable

To construct a square on a given straight line.

c. 300 BCE — Proposition 46, Book I of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

To apply a given parallelogram to a given straight line in a given rectilinear angle.

c. 300 BCE — Proposition 44, Book I of 'Elements' (a problem statement)

Strange & Unusual Unverifiable

A ratio is a sort of relation in respect of size between two magnitudes of the same kind.

c. 300 BCE — Definition 3, Book V of 'Elements'

Strange & Unusual Unverifiable

The greatest of the parts is called the antecedent, and the less the consequent.

c. 300 BCE — Implied from definitions of ratio, not a direct quote.

Strange & Unusual Unverifiable