ROGER BACON (1214- 94)

(Doctor Mirabilis) ‘The Marvelous Doctor’

(Franciscan friar) Oxford – 1257

‘Mathematics (The first of the sciences, the alphabet of philosophy, door & key to the sciences), not Logic, should be the basis of all study’

Converted from Aristotelian to a neo-Platonist.

Etching of ROGER BACON Franciscan friar (1214- 94)


The Multiplication of Species; the means of causation (change) radiate from one object to another like the propagation of light.

‘An agent directs its effect to making the recipient similar to itself because the recipient is always potentially what the agent is in actuality.’

Thus heat radiating from a fire causes water placed near the fire,
but not in it, to become like the fire (hot). The quality of fire is multiplied in the water (multiplication of species).

All change may be analysed mathematically. Every multiplication is according to line, angles or figures. This thinking comes from the ninth century al-Kinde and his thoughts on rays and leads to a mathematical investigation into light.

Fear of the Mongols, Muslims and the Anti-Christ motivated the Franciscans. Franciscan neo-Platonism was based on Augustinian thought with a mathematical, Pythagorean, approach to nature. Bacon subscribed to this apocalyptical view, suffered trial and was imprisoned.
The Dominicans chose Aristotle – with a qualitative, non-mathematical approach to the world.

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1502 – Florence, Italy

‘In the Renaissance science was reinvented’

Image of the VITRUVIAN MAN


Leonardo is celebrated as the Renaissance artist who created the masterpieces ‘The Last Supper’ (1495-97) and ‘The Mona Lisa’ (1503-06). Much of his time was spent in scientific enquiry, although most of his work remained unpublished and largely forgotten centuries after his death. The genius of his designs so far outstripped contemporary technology that they were rendered literally inconceivable.

The range of his studies included astronomy, geography, palaeontology, geology, botany, zoölogy, hydrodynamics, optics, aerodynamics and anatomy. In the latter field he undertook a number of human dissections, largely on stolen corpses, to make detailed sketches of the body. He also dissected bears, cows, frogs, monkeys and birds to compare their anatomy with that of humans.

It is perhaps in his study of muscles where Leonardo’s blend of artistry and scientific analysis is best seen. In order to display the layers of the body, he developed the drawing technique of cross-sections and illustrated three-dimensional arrays of muscles and organs from different perspectives.

Leonardo’s superlative skill in illustration and his obsession with accuracy made his anatomical drawings the finest the world had ever seen. One of Leonardo’s special interests was the eye and he was fascinated by how the eye and brain worked together. He was probably the first anatomist to see how the optic nerve leaves the back of the eye and connects to the brain. He was probably the first, too, to realise how nerves link the brain to muscles. There had been no such idea in GALEN’s anatomy.

Possibly the most important contribution Leonardo made to science was the method of his enquiry, introducing a rational, systematic approach to the study of nature after a thousand years of superstition. He would begin by setting himself straightforward scientific queries such as ‘how does a bird fly?’ He would observe his subject in its natural environment, make notes on its behaviour, then repeat the observation over and over to ensure accuracy, before making sketches and ultimately drawing conclusions. In many instances he would directly apply the results of his enquiries into nature to designs for inventions for human use.

Self portrait of LEONARDO DA VINCI


He wrote ‘Things of the mind left untested by the senses are useless’. This methodical approach to science marks a significant stepping-stone from the DARK AGES to the modern era.

1469 Leonardo apprenticed to the studio of Andrea Verrocchio in Florence

1482 -1499 Leonardo’s work for Ludovico Siorza, the Duke of Milan, included designs for weaponry such as catapults and missiles.
Pictor et iggeniarius ducalis ( painter and engineer of the Duke )’.
Work on architecture, military and hydraulic engineering, flying machines and anatomy.

1502 Returns to Florence to work for Pope Alexander VI’s son, Cesare Borgia, as his military engineer and architect.

1503 Begins to paint the ‘Mona Lisa’.

1505-07 Wrote about the flight of birds and filled his notebooks with ideas for flying machines, including a helicopter and a parachute. In drawing machines he was keen to show how individual components worked.

1508 Studies anatomy in Milan.

1509 Draws maps and geological surveys of Lombardy and Lake Isea.

1516 Journeys to France on invitation of Francis I.

1519 April 23 – Dies in Clos-Luce, near Amboise, France.

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1600 – England

‘Gilbert’s principal area of study related to magnetism, however, his method of enquiry is equally significant’

portrait of WILLIAM GILBERT ©


Gilbert rejected the scholastics’ approach to science, preferring the experimental method, which he applied to the Earth’s magnetic properties.
He carried out some of the first systematic studies of the lodestone in Europe and showed that the Earth acts as a bar magnet with magnetic poles.

His celebrated text, ‘De magnete, magnetisque corporibus, et de magno magnete tellure‘ (On the Magnetic, Magnetic Bodies and the Great Magnet Earth – 1600) is considered to be one of the first truly scientific texts.
Gilbert received his medical training in Cambridge and practiced as a physician in London. He became president of the College of Physicians and was physician to Queen Elizabeth I.

In the time of Elizabeth I and Shakespeare, England was still largely a place of superstition and religious fervor. Gilbert concurred with Copernicus, a potentially dangerous sentiment in an era when elsewhere in Europe others such as Giordano Bruno and later GALILEO were being persecuted (and in the case of Bruno, executed) for sharing the same opinion.

Magnetism was to cast its influence in the eighteenth century, displayed through the electric fluid of GALVANI and VOLTA

He distinguished the properties of magnetism from the attractive effect produced by friction with amber. In so doing he introduced the term that was to become electricity.
He introduced a number of expressions to the English language including: magnetic pole, electric force and electric attraction.
A term of magneto motive force, the gilbert, is named after him.

Gilbert and others postulated that magnetism is the force holding the planets in their orbits.

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1621 – Holland

woodblock print portrait of WILLEBRORD SNELL ©


‘During refraction of light, the ratio of the sines of the angles of incidence ( i ) and refraction ( r ) is a constant equal to the refractive index of the medium’

In equation form: n1sini = n2 sinr 
where n1 and n2 are the respective refractive indices of the two media.

The refractive index of a substance is a measure of its ability to bend light. The higher the number the better light is refracted. The refractive index of diamond, 2.42, is the highest of all gems.

Refraction is the change in direction of a ray of light when it crosses the boundary between two media. It happens because light has different speeds in different media. A ray of light entering a medium where the speed of light is less (from air to water, for example) bends towards the perpendicular to the boundary of the two media. It bends away from the perpendicular when it crosses from water to air. Refraction was known to ancient Greeks, but Snell, a Dutch mathematician, was the first to study it.

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1632 – Italy

‘Discounting air resistance, all bodies fall with the same motion; started together, they fall together. The motion is one with constant acceleration; the body gains speed at a steady rate’



From this idea we get the equations of accelerated motion:
v = at and s = 1/2at2
where v is the velocity, a is the acceleration and s is the distance traveled in time t

The Greek philosopher ARISTOTLE (384-322 BCE) was the first to speculate on the motion of bodies. He said that the heavier the body, the faster it fell.
It was not until 18 centuries later that this notion was challenged by Galileo.

The philosophers of ancient Greece had known about statics but were ignorant of the science of dynamics.
They could see that a cart moves because a horse pulls it, they could see that an arrow flies because of the power of the bow, but they had no explanation for why an arrow goes on flying through the air when there is nothing to pull it like the horse pulls the cart. Aristotle made the assumption that there must be a force to keep things moving. Galileo contradicted. He believed that something will keep moving at the same speed unless a force slows it down.

He contended that an arrow or a thrown stone had two forces acting upon it at the same time – ‘momentum’ pushes it horizontally and it only falls to the ground because the resistance of the air (a force) slows it down enough for it to be pulled to the ground by another force pushing downwards upon it; that which we now know as ‘gravity’.
This is the principle of inertia and led him to correctly predict that the path of a projectile is a parabola.

His insights were similar to the first two of the three laws of motion that Newton described 46 years later in ‘Principia’. Although he did not formulate laws with the clarity and mathematical certainty of Newton, he did lay the foundations of the modern understanding of how things move.

Galileo resisted the notion of gravity because he felt the idea of what seemed to be a mystical force seemed unconvincing, but he appreciated the concept of inertia and realized that there is no real difference between something that is moving at a steady speed and something that is not moving at all – both are unaffected by forces. To make an object go faster or slower, or begin to move, a force is needed.

Galileo would take a problem, break it down into a series of simple parts, experiment on those parts and then analyse the results until he could describe them in a series of mathematical expressions. His meticulous experiments (‘cimento‘) on inclined planes provided a study of the motion of falling bodies.

He correctly assumed that gravity would act on a ball rolling down a sloping wooden board that had a polished, parchment lined groove cut into it to act as a guide, in proportion to the angle of the slope. He discovered that whatever the angle of the slope, the time for the ball to travel along the first quarter of the track was the same as that required to complete the remaining three-quarters. The ball was constantly accelerating. He repeated his experiments hundreds of times, getting the same results. From these experiments he formulated his laws of falling bodies.
Mathematics provided the clue to the pattern – double the distance traveled and the ball will be traveling four times faster, treble it and the ball will be moving nine times faster. The speed increases as a square of the distance.
He found that the size of the ball made no difference to the timing and surmised that, neglecting friction, if the surface was horizontal – once a ball was pushed it would neither speed up nor slow down.

His findings were published in his book, ‘Dialogue Concerning the Two Chief World Systems’, which summarised his work on motion, acceleration and gravity.

His theory of uniform acceleration for falling bodies contended that in a vacuum all objects would accelerate at exactly the same rate towards the Earth.

Legend has it that Galileo gave a demonstration, dropping a light object and a heavy one from the top of the leaning Tower of Pisa. Dropping two cannonballs of different sizes and weights he showed that they landed at the same time. The demonstration probably never happened, but in 1991 Apollo 15 astronauts re-performed Galileo’s experiment on the Moon. Astronaut David Scott dropped a feather and a hammer from the same height. Both reached the surface at the same time, proving that Galileo was right.

Another myth has it that whilst sitting in Pisa cathedral he was distracted by a lantern that was swinging gently on the end of a chain. It seemed to swing with remarkable regularity and experimenting with pendulums, he discovered that a pendulum takes the same amount of time to swing from side to side – whether it is given a small push and it swings with a small amplitude, or it is given a large push. If something moves faster, he realised, then the rate at which it accelerates depends on the strength of the force that is moving it faster, and how heavy the object is. A large force accelerates a light object rapidly, while a small force accelerates a heavy object slowly. The way to vary the rate of swing is to either change the weight on the end of the arm or to alter the length of the supporting rope.
The practical outcome of these observations was the creation of a timing device that he called a ‘pulsilogium’.

Drawing by GALILEO of the surface of the moon

Galileo confirmed and advanced COPERNICUS‘ Sun-centered system by observing the skies through his refracting telescope, which he constructed in 1609. Galileo is mistakenly credited with the invention of the telescope. He did, however, produce an instrument from a description of the Dutch spectacle maker Hans Lippershey’s earlier invention (patent 1608).

He discovered that Venus goes through phases, much like the phases of the Moon. From this he concluded that Venus must be orbiting the Sun. His findings, published in the ‘Sidereal Messenger‘ (1610) provided evidence to back his interpretation of the universe. He discovered that Jupiter has four moons, which rotate around it, directly contradicting the view that all celestial bodies orbited Earth, ‘the centre of the universe’.

‘The Earth and the planets not only spin on their axes; they also revolve about the Sun in circular orbits. Dark ‘spots’ on the surface of the Sun appear to move; therefore, the Sun must also rotate’

1610 – Galileo appointed chief mathematician to Cosmo II, the Grand Duke of Tuscany, a move that took him out of Papal jurisdiction.

1613 – writes to Father Castelli, suggesting that biblical interpretation be reconciled with the new findings of science.

1615 – a copy of the letter is handed to the inquisition in Rome.

1616 – Galileo warned by the Pope to stop his heretical teachings or face imprisonment.

1632 – when Galileo published his masterpiece, ‘Dialogue Concerning the Two Chief World Systems’ – (Ptolemaic and Copernican) – which eloquently defended and extended the Copernican system, he was struggling against a society dominated by religious dogma, bent on suppressing his radical ideas – his theories were thought to contravene the teachings of the Catholic Church. He again attracted the attention of the Catholic Inquisition.
His book took the form of a discussion between three characters; the clever Sagredo (who argues for Copernicus), the dullard Simplicio (who argues hopelessly for Aristotle) and Salviati (who takes the apparently neutral line but is clearly for Sagredo).

In 1633 he was tried for heresy.

‘That thou heldest as true the false doctrine taught by many that the Sun was the centre of the universe and immoveable, and that the Earth moved, and had also a diurnal motion. That on this same matter thou didst hold a correspondence with certain German mathematicians.’
‘…a proposition absurd and false in philosophy and considered in theology ad minus erroneous in faith…’.

Threatened with torture, Galileo was forced to renounce his theories and deny that the Earth moves around the Sun. He was put under house arrest for the rest of his life.

After Galileo’s death in 1642 scientific thought gradually accepted the idea of the Sun-centered solar system. In 1992, after more than three and a half centuries, the Vatican officially reversed the verdict of Galileo’s trial.

Galileo’s thermoscope operated on the principle that liquids expand when their temperature increases. A thermoscope with a scale on it is basically a thermometer and in its construction Galileo was probably following directions given by Hiero of Alexandria 1500 years earlier in ‘Pneumatics’. As with the telescope, Galileo is often incorrectly given credit for the invention of the thermometer.

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1640 – Italy

‘Together with VINCENZO VIVIANI (1622-1703) realised that the weight of air pushing on a reservoir of mercury can force the liquid to rise into a tube that contains no air; that is, a vacuüm’

In 1650 OTTO VON GUERICKE (1602-1686) invented an air pump and showed that if you remove the air from the centre of two hemispheres that are resting together, the pressure of the outside air is sufficient to prevent a team of horses from pulling them apart.

1657 – Formed the Accademia del Cimento with eight other Florentines to build their own apparatus and conduct experiments to advance the pursuit of knowledge. Disbanded after ten years as a condition of its patron Leopoldo de Medici’s appointment as cardinal, its dissolution followed Galileo’s trial by the Catholic Church and marked the decline of free scientific research in Italy.

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BLAISE PASCAL (1623- 62)

1647 – France



‘When pressure is applied anywhere to an enclosed fluid, it is transmitted uniformly in all directions’

EVANGELISTA TORICELLI (1608-47) had argued that air pressure falls at higher altitudes.

Using a mercury barometer, Pascal proved this on the summit of the 1200m high Puy de Dome in 1647. His studies in this area led to the development of PASCAL’S PRINCIPLE, the law that has practical applications in devices such as the car jack and hydraulic brakes. This is because the small force created by moving a lever such as the jacking handle in a sizable sweep equates to a large amount of pressure sufficient to move the jack head a few centimetres.
The unit of pressure is now termed the pascal.

‘The study of the likelihood of an event’

Together with PIERRE DE FERMAT, Pascal developed the theory of probabilities (1654) using the now famous PASCAL’S TRIANGLE.

Chance is something that happens in an unpredictable way. Probability is the mathematical concept that deals with the chances of an event happening.

Probability theory can help you understand everything from your chances of winning a lottery to your chances of being struck by lightning. You can find the probability of an event by simply dividing the number of ways the event can happen by the total number of possible outcomes.
The probability of drawing an ace from a full pack of cards is 4/52 or 0.077.

Probability ranges from 1 (100%) – Absolutely certain, through Very Likely 0.9 (90%) and Quite Likely 0.7 (70%), Evens (Equally Likely) 0.5 (50%), Not Likely 0.3 (30%) and Not Very Likely 0.2 (20%), to Never – Probability 0 (0%).

Picture of the 'Pascaline'. The French mathematician Blaise Pascal invented the a mechanical calculation machine. He called it the Pascaline. The Pascaline was made out of clock gears and levers and could solve basic mathematical problems like addition and subtraction.


The computer language Pascal is named in recognition of his invention in 1644 of a mechanical calculating machine that could add and subtract.


Like many of his contemporaries, Pascal did not separate philosophy from science; in his book ‘Pensees’ he applies his mathematical probability theory to the problem of the existence of God. In the absence of evidence for or against God’s existence, says Pascal, the wise man will choose to believe, since if he is correct he will gain his reward, and if he is incorrect he stands to lose nothing.

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