Leonardo da Vinci's Clockworks

Da Vinci drew and developed many components of clocks, and some designs of entire clocks. These include a variety of gears and escapements, a very accurate three-dial clock for his time, and an alarm clock.

Verrocchio's clay model chosen for the Colleoni monument

Verrocchio worked on his clay model of the Colleoni monument from 1479 to 1483 in competition with other great sculptors of the time. Since Da Vinci began working with Verrocchio in 1466, he played a great role in the creation of this clay model. Da Vinci studied the anatomy of horses, and thus created many detailed sketches for the Colleoni monument. In 1483, Verrocchio's clay model and plans for the statue were chosen as the winner of the competition for the Colleoni monument. Da Vinci's idea for the bronze saving casting process was said to have played a major role in the choosing of Verrocchio's clay model (Kulenovic and von Platten).

Confalonieri prints the first copies of Theophrastus's Historia plantarum

Theophrastus (371 - 287 BC) was a student of Aristotle and is attributed with the title as the father of botany. Theophrastus wrote books on botany such Enquiry into Plants and On the Causes of Plants. In these books, he worked to categorize plants into the groups, study their uses and how to grow them and took note on the anatomy of plants. Based on Theophrastus work we can see how early botanical study revolved around the idea of the usefulness of the plant and trying to create basic distinctions between different plant types. Bartolomeo Confalonieri was the first to print Theophrastus's books in 1483 while in Treviso which allowed much of Europe to learn about his findings. Though it is not known for sure, Theophrastus writing would have been available prior to Leonardo's observations of plants and could have been read by the artist.

Da Vinci Sketches the Viola Organista

Preserved notebooks and sections of the Codex Atlanticus provide various sketches of da Vinci’s concept for a keyboard that can imitate a bowed string instrument. As there were various iterations of the design, the instrument evolves over time. Originally utilizing a mechanized bow, the sketches evolved to include a foot-pedal that controlled wheels to play the strings and ended with a system that would lower individual strings onto an automatic belt in order to make sound. In all, six pages across various manuscripts would be dedicated to the instrument, although none contained enough detail for craftsmen to build a working model from the drawings alone.

The Organista would never be made by da Vinci, as many of these drawings are incomplete. An early sketch of the instrument that utilized a mechanized bow did not show how that bow would be affixed to the instrument. Some drawings included double strings attached to each key (as opposed to the typical one per key), likely to increase the volume of the instrument. Ultimately, da Vinci’s drawings were rather difficult to decipher when attempting to envision a singular model of the device.

Raccolta Vinciana. (n.d.). Retrieved May 14, 2019, from https://bibdig.museogalileo.it/Teca/PDFProvider?pdf=/./000/000/337/33723...

Da Vinci, L. (2011, March 16). Viola organista [Digital image]. Retrieved from https://commons.wikimedia.org/wiki/File:Viola_organista.jpg

Da Vinci Completes Sforza Monument Clay Model

Da Vinci's initial works contained too abstract ideas and could not be cast into bronze with a single pour, retendering them incompletable. In his first two main designs, he had a horse rearing up over a fallen foe (Hanson, 2012). Although the fallen foe aided with the stability of the horse, it prohibited a single pour casting. His third design significantly differed from the other two, as it did not contain the fallen foe and was in a frozen trot with two suspended legs (Hanson, 2012). By 1490, Da Vinci began more intense work on the monument and completed a 24-foot clay model of a more detailed version of his third design by 1493, which sat in the Cortile Vecchio of the Castello at Milan (Grierson, 1959). Before Da Vinci’s attempt with his clay horse, no one had created such an equestrian statue with two suspended legs. One suspended leg, as in the Colleoni monument, poses a great challenge with stabilizing the center of gravity; having two suspended legs further heightens this challenge. 

To account for the instability of the statue with two airborne legs and to protect it against several environmental factors, Da Vinci had an intricate structure of the horse. He designed the inside of the horse to have a steel “skeletal structure,” essentially trusses within the horse, and thick metal walls (Ahl, 1995, p. 136). Even though such framing led to other problems, it miraculously maintains the structure of the horse. Such a comprehensive design stands as a feat for the 1400s and 1500s. 

Ahl, D. (1995). Leonardo da Vinci's Sforza monument horse: The art and the engineering. Bethlehem [Pa.]: London; Cranbury, NJ: Lehigh University Press; Associated University Presses.

Grierson, P. (1959). ERCOLE D'ESTE AND LEONARDO DA VINCI'S EQUESTRIAN STATUE OF FRANCESCO SFORZA. Italian Studies, 14(1), 40-48.

Hanson, E. J. (2012). Inventing the sculptor: Leonardo da Vinci and the persistence of myth (Doctoral dissertation, Washington University) [Abstract]. All Theses and Dissertations (ETDs),765. doi: https://doi.org/10.7936/K7PN93MQ

Pacioli's First Publication

In 1494 Luca Pacioli (a Franciscan monk and geometer) traveled to Venice to publish Summa de arithmetica, geometria, proportioni et proportionalita, which had the goal of being a comprehensive summary of mathematical knowledge at the time. Almost none of the mathematics featured was Pacioli’s original work, but he did give credit to those who produced the results he mentioned, which included thinkers like Euclid, Boethius, Sacrobosco, and Fibonacci . It had a completely summary of Euclid’s Elements and it studied games of chance (Pacioli presented an attempt at a solution to a problem in this subject which was later deemed incorrect). A revolutionary aspect of this text is that it was published in Italian (the vernacular), not Latin.  The publishing of this work also established Pacioli’s name in the academic and intellectual communities at the time, most definitely catching the attention of da Vinci (who bought a copy as soon as it was published). It is reasonable to speculate that da Vinci recruited Pacioli to the Milan court because he was so impressed by this work.

Sources

Isaacson, Walter. Leonardo Da Vinci. Simon & Schuster Paperbacks, 2018.

“Luca Pacioli.” Luca Pacioli (1445-1517), School of Mathematics and Statistics, University of St. Andrews, Scotland, www-history.mcs.st-and.ac.uk/Biographies/Pacioli.html.

The image source is Wikimedia Commons, and it is in the public domain in the United States because it was published (or registered with the U.S. Copyright Office) before January 1, 1924.

Colleoni Equestrian Statue Monument Inauguration

After being chosen as the winner of the Colleoni equestrian statue monument, Verrocchio spent five years working on the statue until he died in 1488. By this time, Da Vinci no longer lived in Venice, as he had moved to Milan in 1482 to work for Lodocivo Sforza, the Duke of Milan. As such, the state of Venice handed off the Colleoni monument project to Da Vinci's competitor, Alessandro Leopardi, who was a sculptor and architect (Kulenovic and von Platten). Using Verrocchio and Da Vinci's initial designs as well as his own, Leopardi finished the monument and placed his name on the statue base. Finally, the Colleoni equestrian statue monument was inaugurated in 1496 and still stands, as a feat of art and engineering, in front of the San Giovanni e Paolo church today.

Completion of the Last Supper

Three years after the painting’s commission, Last Supper was completed. A digital reconstruction of what the painting might have looked like when it was finished reveals rich colors and captivating details that are barely visible today. da Vinci’s use of perspective in this painting is ingenious, and he was able to effectively use many new Renaissance techniques to create a vibrant and impactful masterpiece.

               The central vanishing point of the painting is directly behind Jesus’s head, drawing the viewer towards the main subject of the painting. Close examination reveals that da Vinci actually hammered a nail into the center of the wall and cut thin incisions radiating out that guided his painting lines and helped his accuracy. However, the perspective is not perfect because the painting is so large that it appears different depending on the viewer’s vantage point as the viewer is closer to some parts of the painting than others. To remedy this issue, da Vinci applied complex perspective, using a mix of natural and artificial perspective, as well as optical tricks to minimize distortion. He designed the painting so that the perspective appears perfect when viewed from a door in the right wall, where the monks entered the refectory. He then created an artificial ideal vantage point 30 feet from the wall, at eye level with Jesus, again emphasizing Jesus as the focus of the painting. In the painting, da Vinci used the table to hide the lines where the floor hits the back and side walls, and he painted a cornice that hides the fact that the ceiling doesn’t extend all the way above the table. This effective use of optical tricks and complex perspective shows “his mastery of complex rules of natural and artificial perspective, but it also shows his flexibility at fudging those rules when necessary” (Issacson p. 281).

               da Vinci also used newer painting ideas to create his masterpiece. Standard linear perspective had been well studied at the time, but “Leonardo’s most important contribution to the study of perspective was to broaden the concept to include not just linear perspective...but also ways of conveying depth through changes in color and clarity” (Issacson p. 274). Da Vinci included three windows in the back of the painting that look out into the far distance of a mountain range, and one can clearly see the blurriness and blueness of the mountains as a fantastic example of his aerial perspective. One can also see the impressive blue gradient of the sky, sfumato that adds to the realism of the painting. The windows extend the three dimensional space seemingly into infinity, contrasting the flatness of many previous paintings.

Jesus and the disciples surrounding him possess incredibly expressive emotion and vibrant, rippling movement. da Vinci continuously studied how to portray emotions using body language and gestures, believing that “‘a picture of human figures ought to be done in such a way as that the viewer may easily recognize, by means of their attitudes, the intentions of their minds’” (Issacson p. 282). Through his intensive human studies and detailed portrayal of his figures’ emotions, he uses the Renaissance concepts of naturalism and humanism to pay homage to the complexity of the human form and mind. da Vinci’s choice to not include any gold halos or gold background also helps focus on the human forms of the figures through its removal of anagogic space.

Finally, da Vinci incorporated the revolutionary concept of involving the viewer in the painting by adjusting the lighting in the painting – the light appears to come from an actual window high on the left wall of the refectory, which blends reality and imagination and involves the viewer in the painting.

               While da Vinci used many of these new and complex techniques, he also referenced past versions of The Last Supper through his decision to put all of the figures on the back side of the table. He was certainly capable of painting people on both sides of the table, but putting them all on one side maintains this tradition and does not shock viewers with its boldness. At the same time as he is referencing the past, he incorporates new ideas as the figure placement also allows the viewer to clearly see Jesus and each disciple’s face, body, and movements, emphasizing their emotions as da Vinci wanted and adding to the effect of the viewer being included in the painting.

Sources:

Leonardo da Vinci's Last Supper. (June 21, 2012). Retrieved from http://www.italianrenaissance.org/a-closer-look-leonardo-da-vincis-last-supper/

Issacson, W. (2017). The Last Supper. In Issacson, W, Leonardo da Vinci. (pp. 273-292). New York, NY: Simon & Schuster

Image Sources:

Bando, K. (2016). Digital Reconstruction of The Last Supper. [Image]. Retrieved from http://www.leonardoresearch.com/The%20Last%20Supper.html

The Last Supper Perspective (n.d.) Retrieved from https://www.leonardodavinci.net/the-last-supper.jsp#prettyPhoto

French Army Destroys Sforza Monument Clay Model

Da Vinci's clay model of the Sforza monument horse was a feat of engineering, with two horse legs suspended and a total height of 24 feet. It remained standing in the Cortile Vecchio of the Castello at Milan until it was destroyed in 1499. It is believed that when the French army came across the statue they brutally destroyed it, using it as "target practice" (Grierson, 1959, p. 40). The French army's destruction was the ultimate factor in the incompletion of the monument. Since Da Vinci died in 1519, he never recreated the clay model and his horse was not attempted until centuries later with greater advancements in technology. Thus, his brilliance and Renaissance combination of art and engineering were not fully realized and appreciated until centuries later.

Leonardo da Vinci Designs Arched Bridge

Leonardo da Vinci was a proficient engineer as well as artist, and among his designs was a bridge entirely supported by the parabolic arch underneath it. His notebook includes two illustrations of this arched bridge. He specified that the bridge, which would span the Golden Horn connecting Galata to Istanbul, would be 600 braccia long, which is equivalent to 366 m or 1200 ft; 400 braccia spanned the inlet itself, with 100 braccia over the land on either side. At its highest point, the arch would rise 70 braccia, or 43 m, above the water. While da Vinci was correct in asserting that a parabolic shape would offer extraordinarily strong support, the exact mathematical techniques required to build a bridge of this design were not developed until centuries later. These sketches, found in Manuscript L, are currently located at the Institut de France in Paris.

Sources:

Atalay, B. (2013, January 22). LEONARDO’S BRIDGE: Part 2. “A Bridge for the Sultan”. Retrieved May 11, 2019, from https://blog.nationalgeographic.org/2013/01/22/leonardos-bridge-part-2-a...

Books, Maps and Calligraphic documents in the Topkapi Museum. (n.d.). Retrieved May 12, 2019, from http://kilyos.ee.bilkent.edu.tr/~history/booknmaps.html

C. (2011, April 10). Bridge built using Leonardo da Vinci's design for a self supporting bridge.Retrieved May 12, 2019, from https://commons.wikimedia.org/wiki/File:Leonardo_da_Vinci_bridge_Karby.jpg (Originally photographed 2011, April 10)

The image is from Wikimedia Commons and taken by user Cntrading. It is used with the Free Art License.

Letter to Sultan Beyazid II of Istanbul

While in Florence around 1502 or 1503, Leonardo da Vinci pursued a position as a scientist and engineer in the court of Sultan Beyazid II of Istanbul. To showcase his innovative ideas, he sent a “cover letter” to the Sultan proposing four projects: a windmill, a hydraulic pump, a bridge connecting Galata to Istanbul, and a suspension bridge across the Bosporus connecting Turkey and Asia. The bridge connecting Galata to Istanbul across the Golden Horn was da Vinci’s first formal proposal for a self-supporting arched bridge. As proposed, the bridge would be the longest single span bridge at the time and self supporting due to the parabolic shape of the arches underneath it. The sultan rejected this radical proposal and da Vinci’s design remained unused. The connection between this letter and da Vinci's sketches of the arched bridge design was established in 1952, as the letter, stored in the Istanbul National Archives, had been mislabeled and misattributed. The letter is now on display in the Topkapi museum in Istanbul.

Sources:

Atalay, B. (2013, January 22). LEONARDO’S BRIDGE: Part 2. “A Bridge for the Sultan”. Retrieved May 11, 2019, from https://blog.nationalgeographic.org/2013/01/22/leonardos-bridge-part-2-a...

Erik Cleves, K. (2014, April 8). [Galata]. Retrieved May 11, 2019, from https://commons.wikimedia.org/wiki/File:Galata_(13971741453).jpg

The image was taken by Erik Cleves Kristensen and is licensed under the Creative Commons Attribution 2.0 Generic license. It is provided through Wikimedia Commons.

Map of Valdichiana Valley

This map was supposedly created when the Da Vinci was still in service of Cesare Borgia. Yet there is evidence that there was little military purpose. While the locations all have names, the rivers are detailed with names as well. Many believe that Da Vinci created the map to build a canal from Florence to the sea. Using the map created, one could plan a dam for Lake Chiana, allowing the canal to be used even during the dry season. Due to this fact, the map seems to serve a more commercial purpose. Alas, it could also be used for transporting soldiers and equipment as well. As the canal was never made, the purpose of the map, or the canal, is not truly known.

Sources:

“Map of Tuscany and the Chiana Valley.” Web Gallery of Art, wga.hu/html_m/l/leonardo/13maps/2tuscany.html.

“A Map of the Valdichiana.” Royal Collection Trust, www.rct.uk/collection/912278/a-map-of-the-valdichiana.

Leda and the Swan

Leda and the Swan is a painting completed by Leonardo da Vinci in 1508. The completed work of art displays highly detailed images of plants. The plants da Vinci draws are unlike most of those seen in other artists paintings prior to this time. The Pre-Renaissance era of art marked a time when plants were shown as being distinct from each other but only slightly. Da Vinci was one of the first to portray plants in a very organic lifelike manner. In preparation for painting Leda and the Swan, Leonardo completed many studies and sketches of plants that then lead him to write down his observations in his notebooks. The original Leda and the Swan was lost but has since been recreated and now is displayed in the Uffizi.

image from Wikimedia Commons, commons.wikimedia.org/wiki/File:Leda_Melzi_Uffizi.jpg and within the public domain and fair use.

Raphael Sketches the Mona Lisa

The Mona Lisa had a very large effect on daVinci's contemporaries, especially Raphael. It can be seen in numerous Raphael paintings that he took large inspirtion from the portrait. His "Yound Woman with a Unicorn" is exremetly similar to the Mona Lisa, with folded hands, three quarter tilt, and mysterious smile. However, he also drew an early version of the Mona Lisa, as noticible differences between the sketch and the final product are evident. 

Leonardo Creates Detailed Sketches of Plants

While working on his painting Leda and the Swan, Leonardo created several sketches of plants, such as A star-of-Bethlehem and other plants (c.1506-12), in order to better represent them within his painting.  Sketches These sketches show a high level of detail that later carries into his art and pays close attention to the form and structure of plants and how that can change for each one. These sketches have been collected and held on to by the Windsor Castle Royal Collection since the 17th Century.

Image from Wikimedia Commons, commons.wikimedia.org/wiki/File:Leonardo_da_vinci,_Star_of_Bethlehem_and_other_plants.jpg. This image is under public domain and free use.

Mapping a New World

With the discovery of the Americas, new world maps had to be drawn and with the knowledge that the Earth is not flat, many cartographers struggled with the representing the continents as they physically were. Da Vinci took a new approach of making 2, 4-leaf clovers next to each other to create the map. For many, this was a revolutionary idea. The Arctic was shown as a sea and the Antarctic was shown as a continent, concepts that were newly discovered at that time as well. Additionally, Da Vinci was the first to use the word America. Most of his depiction was based on information from Amerigo Vespucci. Still, there were some in accuracies in the map as Da Vinci had not perfected the perspective needed. Europe is enlarged to a great degree. Da Vinci’s approach was a step in the right direction however, as the rectangular map was extremely inaccurate at that time, and even today.

Sources:

Chepkemoi, Joyce. “What Was Leonardo's World Map?” WorldAtlas, 5 June 2017, worldatlas.com/articles/what-was-leonardo-s-world-map.html.

“Leonardo Da Vinci's Mappamundi.” ODT Maps, www.odtmaps.com/behind_the_maps/amundi-map-details.asp.

Codex Leicester

Page from the Codex Leicester

The Codex Leicester, later renamed the Codex Hammer, was one of da Vinci's many scientific journals. It was published in 1510 and its contence mainly focused on his ideas on water and the moon.  An interesting note about this text is the "mirror image" style it is written in, meaning that it should be read from right to left, appearing normally in its reflection.  The Codex als holds the record for the second largest price tag, purchased by Bill Gates in 1994 for $30.8 million dollars, making the manuscript also the only of da Vinci's journals to be privatly owned.

Heliocentric Theory

Geocentric model vs Heliocentric model

Although he was not the first to propose the concept, Copernicus is considered the father of the heliocentric model of the universe, claiming that the sun was the center of the universe rather than the sun.  This discovery was highly controversial, and Copernicus therefore published his work on his deathbed in fear of retribution from the church.  Along with this theory, he also incorrectly claimed that stars are immovable and Earth orbited in a sphere, however, his ideas were still revolutionary.  His ideas were also built upon by future scientists such as Brahe and Kepler who were able to mathematically fix some of Capernicus' miskates such as the distance of stars from Earth and the shape of a plant's orbital.  Similar to the invention of the telescope, Copernicus published his work after da Vinci's death, meaning the theories da Vinci made on the mood originated with the assumption that the Earth was the center of the universe.

Romorantin Palace

In 1517, Leonardo was asked to design a new palace in France, where he had moved shortly after the fall of Sforza in 1499. The palace that he designed was vast and extravagant, and it had several similarities to the ideal city that he had designed years before. The palace would sit alongside a river, which would allow for a small network of canals to be constructed. The designs included two large, square-shaped palaces and enough smaller buildings around them to make a small village. Unfortunately, in 1519, Leonardo da Vinci passed away, and though his designs were mostly complete, they were abandoned. Because of this, many of his plans for the palace were lost over time, and extensive research has been done to try to recover the missing pieces of his design.

Source and Photo Source: http://www.leonardo-da-vinci.net/romorantin-palace/

The "Real" Father of Anatomy

It is Andreas Vesalius, not Leonardo da Vinci, that is known as the Father of Anatomy and is mentioned in modern anatomy books today. Vesalius was an anatomist and physician from Brussels. He published “De humani corporis fabrica” (translated to “On the Fabric of the Human Body”) in 1543, which is known as the first modern anatomy textbook. Vesalius’s book followed many of da Vinci’s previous studies and challenged dogmas set by previous anatomist Galen. Many of Galen’s observations were related to old theory (humorism) and animal dissections, since human dissections were outlawed by Roman Law. Vesalius was able to get his hands on a few human cadavers and rectified some of Galen’s errors, such as the thought the heart contains the great vessels of the body versus the liver. Vesalius was also the “first” to note that bones gave humans their shape and depicted this through detailed drawings of bone, ligament, and muscle. Vesalius described many body systems in extraordinary detail, which was thought to never have been done before. But da Vinci made extraordinary advances and detailed notebook entries of anatomy years before Vesalius was even born. Da Vinci used his artistic ability and mind for mechanics to create detailed drawings of the human body and body systems. Some of his most infamous drawing and notes were related to muscle/ ligaments, the heart, skull, and fetus. His talent as an artist won him opportunities to dissect over 30 cadavers (compared to Vesalius’s few), allowing him to prove Galen wrong years before Vesalius. Unfortunately, da Vinci’s works were never published, so his genius had little impact on the advancement of anatomy.

Sources:

Bridges, C.D. (2015). Biology 201/203: Human Anatomy and Physiology. Plymouth, MI. Hayden-McNeil.

Toledo-Pereyra, L.H. (2009). Leonardo da Vinci: The Hidden Father of Modern Anatomy. Journal of Investigative Surgery, 15(5), 247-249).

More modern notions of geometry and space developed

The hypercube, a four-dimensional shape

During these centuries, the mathematical understanding of geometry and space expanded from the plane to n-dimensional Euclidean space and non-Euclidean space. Although none of Euclid’s Elements was deemed incorrect, during the 17^th century mathematicians Desargues and Pascal realized that Euclidean geometry was a special instance a more general type of geometry: projective geometry. However, the work of these two mathematicians was not given much attention until the 19^th century when their works were rediscovered independently by geometers of that time. Further, the 19^th century saw a greater expansion and generalization in the understanding of geometry: the works of Gauss, Riemann, and others developed ideas like the manifold (objects that behave locally like Euclidean space) and curved spaces. Likewise, instead of working in the plane mathematicians were concerned with the aforementioned generalized spaces. More importantly, these new conceptions of space became well-established in standard mathematical instruction by the end of the 19^th century.   

Sources

Kline, Morris. “Projective Geometry.” Scientific American, vol. 192, no. 1, 1955, pp. 80–86., doi:10.1038/scientificamerican0155-80.

Shearer, Rhonda Roland. “Chaos Theory and Fractal Geometry: Their Potential Impact on the Future of Art.” Leonardo, vol. 25, no. 2, 1992, pp. 143–152., doi:10.2307/1575702.

The image is from Wikimedia Commons and in the public domain. 

The Moon's Surface

After making vast improvments in the telescope in 1609, Galileo was able to make detailed observations of various planets as well as the moon.  One such observation was that the moon was not the perfect spherical surface society assumed it to be, but rather was made up of various valleys, plains, and moutains much like the Earth's surface.  This gave further insight into da Vinci's observations on the various dark spots scattered throughout the moon's surface.  These discoveries were particularly radical since the moon, like the planets, were through to be perfect celestial beings and the thought of them containing imperfections would have been highly controversial.

Further Destruction

With Last Supper already in disrepair, in 1652 monastery residents cut a door into the middle of the painting, removing Jesus’ feet and creating the large gray space seen in the bottom of photos of the painting. Later in the 1700s, soldiers of Napoleon Bonaparte turned the refectory into a stable and used the painting as target practice for projectiles. During World War II, the Nazis bombed the monastery, but the painting was luckily protected by sandbags so was not completely destroyed. However, all of this clearly did not help the already-flaking painting.

Sources:

The Last Supper – by Leonardo da Vinci. (2011). Retrieved from https://www.leonardodavinci.net/the-last-supper.jsp

Issacson, W. (2017). The Last Supper. In Issacson, W, Leonardo da Vinci. (pp. 273-292). New York, NY: Simon & Schuster

Lenormand's Parachute

Parachute Descent

Sebastien Lenormand is considered to be the first person to make a fully functioning parachute (or at least the first one that was well documented). He jumped from the top of the tower within the Montpellier Observatory in France and safely landed. This parachute was 14 feet. This mechanism was intended to be a portable fire escape, allowing people to escape buring buildings. The jump is recorded to have occured in December of 1783.

Source: Britannica, T. E. (2019, January 01). Louis-Sebastien Lenormand. Retrieved from https://www.britannica.com/biography/Louis-Sebastien-Lenormand

Image Scorce: Louis-Sébastien Lenormand. (2019, February 05). Retrieved from https://en.wikipedia.org/wiki/Louis-Sébastien_Lenormand