# Let's learn some Math!

## Discover a Portuguese way to teach Mathematics, Physics and Astronomy by using didactic tiles from 17th century

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

These azulejos, or wall tiles, were made probably in Coimbra to satisfy the instructions issued by the Superior-General of the Society of Jesus in 1692, aimed at the improvement of the quality of mathematics teaching in Portugal. However, recourse to visual memory also served astronomy and physics. The geometric figures were a faithful reproduction of the teaching version of “Elements”, a work by Euclid, published in 1654 by the Jesuit André Tacquet. In 1836 the walls of the refectory of the College of Jesus in Bahia, still supported tiles identical to these.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book I | Definition 31

A rectangle is a quadrilateral figure, with 4 right angles, therefor equals, whether or not the sides are equal.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book I | Proposition 29

A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the sum of the interior angles on the same side equal to two right angles.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book I | Proposition 44

To a given straight line [OS] in a given rectilinear angle [X], to apply a parallelogram equal to a given triangle [V].

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book III | Proposition 25

Given a segment of a circle, to describe the complete circle of which it is a segment.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book VI | Proposition 3

If an angle of a triangle is bisected by a straight line [BF] cutting the base, then the segments of the base [AF,FC] have the same ratio as the remaining sides [AB, CB] of the triangle; and, if segments of the base [AF,FC] have the same ratio as the remaining sides of the triangle, then the straight line joining the vertex to the point of section bisects the angle of the triangle [B].

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book XI | Definition 5

The inclination of a straight line [LO] to a plane is, assuming a perpendicular drawn from the end of the straight line [L] which is elevated above the plane to the plane, and a straight line joined from the point thus arising to the end of the straight line which is in the plane, the angle [LOP] contained by the straight line [BO] so drawn and the straight line standing up.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Book XII | Propositions 14-15

Cones and cylinders on equal bases are to one another as their heights. In equal cones and cylinders the bases are reciprocally proportional to the heights; and those cones and cylinders in which the bases are reciprocally proportional to the heights are equal.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

From Archimed Theorem | Proposition 20

Conical superficies inscribed in a sphere, length end in the superficies of the sphere.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

This tile represents the Universes's Ptolemaic system.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Evidence of the passage of the comet Helvius in 1652. Bellow we can see a little bit of what we think might be the Copernico's Universe System.

‏‏‎ Wall tile for teaching purposes (18th century)Museu Nacional de Machado de Castro

Some constellations: Scorpio and Saggitarius [symbolised by the arrow, just bellow Scorpio].

Take a walk in the museum and search for the tiles that teach!

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Photo: DGPC/ADF - Photographic Documentation Archive

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