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Francesco Maria Grimaldi  
  
1461   01:46 صباحاً   date: 19-1-2016
Author : D Graves
Book or Source : Scientists of faith: forty-eight biographies of historic scientists and their Christian faith
Page and Part : ...


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Date: 24-1-2016 1109
Date: 25-1-2016 1180
Date: 24-1-2016 1380

Born: 2 April 1618 in Bologna, Papal States (now Italy)
Died: 28 December 1663 in Bologna, Papal States (now Italy)

 

Francesco Grimaldi was born into a well-off family. His father, Paride Grimaldi, was a silk merchant of noble birth who had moved to Bologna in 1589. He married in Bologna, but the couple were childless when his wife died. In about 1614, Paride Grimaldi married his second wife, Anna Cattani, who owned a chemist shop which she had inherited from her grandfather. Francesco was the fourth of his parents six sons, five of whom survived. He had two older brothers (one child having died), the one that he was closest to being Vincenzo Maria Grimaldi who was almost exactly one year older. When Francesco was still quite young, his father died and, at that time, his mother took over running the family chemist shop. Francesco and his brother Vincenzo both joined the Society of Jesus (the Jesuits) on 18 March 1632.

We do not know all the places where Grimaldi studied, in particular we are unsure where he spent the two years 1632-34 although it was most likely in Novellara. We know for certain that in 1634 he was in Novellara, about 20 km north of Reggio dell'Emilia, where he lived in the house which had been set up in 1571 for training Jesuit novices. In 1635 he went to Parma, just over 30 km to the west of Novellara, where he began his study of philosophy. The Jesuits ran three educational establishments in Parma, the university, a college for educating the sons of the nobility, and a Jesuit College, established around 1600, which Grimaldi attended. In addition to advanced courses in philosophy and theology, the College provided lower level courses in grammar and rhetoric. However, he was in Parma for less than a year before he was transferred to Bologna to complete his first year of study of philosophy. His second year studying philosophy,1636-37, was spent at Ferrara before he returned to Bologna to finish the three year course in session 1637-38. Having completed the three year philosophy course, he taught rhetoric and humanities in the College of Santa Lucia at Bologna for four years from 1638 to 1642. Grimaldi was taught by Giovanni Battista Riccioli in Parma in 1635 and both had moved to Bologna at the same time in 1636. However, it was when Grimaldi returned to Bologna and was teaching there in 1640 that he began assisting Riccioli with experiments. Grimaldi, working under instruction from Riccioli, dropped weights from the Asinelli tower and timed their fall using a pendulum. Riccioli was hoping that the experiments conducted by Grimaldi would refute Galileo's theories, which in some sense they did. Let us look in a little more detail at the experiment.

First, Grimaldi and Riccioli calibrated a pendulum by getting it to swing for 24 hours (measured by the star Arcturus crossing the meridian line). They used this 3 foot pendulum to calibrate a shorter pendulum to use in timing. Then Grimaldi dropped balls of wood and of lead from various heights from the Asinelli tower. A nice addition to the accuracy was obtained by getting a group of musical monks to chant in time with the swinging pendulum to aid with the timing. The experiment did not confirm Galileo's result for, as one might expect, the lead balls reached the ground before the wood ones in all the experiments using different heights on the tower [11]:-

As everyone had expected, Galileo was disproved. The lead ball always hit the ground before the wooden one when they fell from the same height. The discrepancy between the experiment and Galileo's claim that they reached the bottom simultaneously was so great that Grimaldi supposed that Galileo must have known about it, but suppressed his knowledge in order to secure a proposition dearer to him than truth.

Over the next few years Grimaldi continued studying but also worked, particularly on astronomical investigations, with Riccioli. He studied theology between 1642 and 1645 going on to undertake further research on philosophy which led to him being awarded a doctorate in 1647. He then began to teach philosophy but, after less than a year, he had changed topics and began to teach mathematics. It is not entirely clear what prompted the change. Many historians suggest that the change of topic was a result of health problems, and he found teaching mathematics less demanding than teaching philosophy. However, this seems somewhat unlikely and it would appear that he may have been eased out of teaching philosophy due to his views being too "modern". Remember that he was still within the Jesuit educational system. Certainly Riccioli, who wrote an obituary of Grimaldi, states clearly that:-

... Grimaldi was well prepared to teach all branches of mathematics: geometry, optics, gnomonics, statics, geography, astronomy and celestial mechanics.

Grimaldi was ordained a priest on 1 May 1651. In the same year Riccioli published Almagestum novum in which he credited Grimaldi with being the source of over 40 different experiments. For example, the experiment of dropping weights from the Asinelli tower is described, and an experiment firing a cannon ball in different directions. This last experiment is quoted as follows [11]:-

The argument against the Diurnal and Annual Motion of the Earth devised by Father Francisco Maria Grimaldi based on a cannon ball fired into the North, and into the East and West.

As another example, we quote again from Almagestum novum [11]:-

P Francisco Maria Grimaldi and I have developed a method for reliably measuring the apparent diameters of the stars by means of a telescope.

Of course, this "reliable method" is no more than a property of the telescope and is measuring the brightness rather than the diameter of the stars. Believing that they were measuring diameters caused them, and others at this time, to have completely incorrect idea of the actual sizes of the stars. Grimaldi and Riccioli's astronomical observations had been made in an observatory set up at the College of Santa Lucia in Bologna. In the Almagestum novum Riccioli thanks the "diligent, prudent, and faithful" Grimaldi. He says that he was too old to conduct the required late-night observations himself, so he had to rely on his young collaborator Grimaldi. Another important chapter in Almagestum novum presented maps of the moon's surface made by Grimaldi and containing names for the major features on the surface, named after famous scientists (particularly astronomers), which have been adopted today [1]:-

An especially noteworthy contribution was his selenograph of the moon, a composite from telescopic observations of many phases, accurate and correct enough so that he must have used crossed hairs and a micrometer with his eyepiece.

Another project on which Grimaldi worked was a survey, using triangulation, to determine a meridian line for Bologna. Again he collaborated on this with Riccioli but, in addition, he was assisted by Ovidio Montalbini (1601-1672), a professor at Bologna University and the custodian of its science museum, and Giovanni Domenico Cassini, who had been appointed as professor of mathematics at the University of Bologna in 1650 following the death of Bonaventura Cavalieri. The project was completed by 1655 and the results published, again by Riccioli, in Geographiae Hydrographiae Reformatae (1661). Grimaldi did a considerable amount of observing and the data from his observations of stars was published in Riccioli's Astronomia Reformata (1665).

Now although we have given quite a lot of information about Grimaldi's work, everything we have mentioned so far was published in works by Riccioli. In fact Grimaldi has no works published under his own name during his lifetime. He died of a sudden illness at the age of 45 but he had spent the last ten years of his life undertaking remarkable research on the properties of light. His work on light was so novel that it had a much smaller impact than one might have expected. He completed writing Physico-Mathesis de Lumine shortly before his death and it was published in 1665. The work is an attempt by Grimaldi to determine whether light is a substance or whether it is a quality of another substance. He does this in a rather unusual way. The treatise consists of two books, the first puts forward arguments that light is a substance, although it does sometimes put the opposing view, while the second book argues that light is a quality of another substance. Grimaldi makes it clear that his own view is that light is not a substance and he believes that the arguments in the second book make it probable that light is a quality. Both books, however, have a common feature; they both argue against a corpuscular theory of light.

Book 1 begins with a description of Grimaldi's most famous discovery, namely the diffraction of light. He created a pinhole through which he allowed light from the sun to enter a darkened room and fall on a screen. The screen was at an angle so that the light produced a elliptical image on the screen. He placed a thin rod in the path of the light and measured the size of the shadow on the screen. He discovered that the shadow was larger than it should have been given conical nature of the beam. From this he argued that this effect was impossible if light consisted of corpuscles so light must have a fluid form which bent round the object. He also noticed coloured bands near to the shadow of the rod. Each band had three components, a white broad central part with a narrow violet band on the side nearest the shadow with a narrow red band on its side furthest from the shadow. He then described what effect was produced by placing obstacles of a different shape from the rod in the path of the cone of light. The name diffraction was chosen by Grimaldi because the effect reminded him of how a flowing fluid splits apart when a thin stick is placed in its path - the Latin diffractio means to "break apart". After treating diffraction, he looked at interference by allowing the light to enter the darkened room through two pinholes and observing where the images overlapped on the screen. He announced with the following proposition:-

That a body actually enlightened may become obscure by adding new light to that which it has already received.

Next Grimaldi treated reflection, refraction, and the propagation of light. What we have so far described takes up about one half of the first book. The second half of this book is concerned with colours and the rainbow.

Perhaps surprisingly, Grimaldi's treatise was little read but his important results on diffraction were made widely known by others. A Rupert Hall writes [13]:-

Grimaldi's experiments and ideas were disseminated by others, not least by the Lyons Jesuit Honoré Fabri (1607-88), a man whose writings, especially those on pure mathematics, were well known. Isaac Newton, by his own affirmation, learnt of the diffraction effect from the first dialogue in Fabri's 'Dialogi physici' (1669).

Honoré Fabri's Dialogi physici sex quorum primum est de Lumine has as its first dialogue 96 pages containing the description of Grimaldi's experiments. Fabri, however, did not believe Grimaldi's "explanation" of the results obtained and attempted to give his own interpretation. The importance of Grimaldi's experiments in influencing the work of Newton is discussed by Roger Stuewer in [15]. It is worth noting that Grimaldi's attempt to explain diffraction was incorrect, as was the attempt of every scientist until Joseph von Fraunhofer (1787-1826) in the 19th century.


 

  1. B S Eastwood, Biography in Dictionary of Scientific Biography (New York 1970-1990). 
    http://www.encyclopedia.com/topic/Francesco_Maria_Grimaldi.aspx

Books:

  1. D Graves, Scientists of faith: forty-eight biographies of historic scientists and their Christian faith (Kregel Publications, 1996).
  2. F A McGrath, Grimaldi's Fluid Theory of Light (M.Sc. dissertation, University College, London, 1969).
  3. E H Oakes, Encyclopedia of World Scientists, Volume 1 (Infobase Publishing, 2007).
  4. R Savelli, Grimaldi e la rifrazione (Bologna, 1951).
  5. R Savelli, Nel terzo centenario del 'De lumine' di F M Grimaldi (Ferrara, 1966).
  6. G Tabarroni, P F M Grimaldi Bolognese iniziatore della ottica-fisica (Bologna, 1964)
  7. G Tabarroni, Nel terzo contenario della morte de F M Grimaldi (Bologna, 1964).

Articles:

  1. U Baldini, Riccioli and Grimaldi (Italian), in Giambattista Riccioli and the scientific merit of the Jesuits in the Baroque period (Italian), Ferrara/Bondeno, 1998 (Olschki, Florence, 2002), 1-47
  2. H Brock, Francesco Maria Grimaldi, in The Catholic Encyclopedia (Robert Appleton Company, New York, 1910). 
    http://www.newadvent.org/cathen/07034a.htm
  3. C M Graney, 126 Arguments Concerning the Motion of the Earth, as presented by Giovanni Battista Riccioli in his 1651 'Almagestum Novum'. 
    http://arxiv.org/pdf/1103.2057.pdf
  4. Francesco Maria Grimaldi, The Supplement to the Penny Cyclopædia of the Society for the Diffusion of Useful Knowledge (C Knight, London, 1851), 667-668.
  5. A R Hall, Beyond the fringe: diffraction as seen by Grimaldi, Fabri, Hooke and Newton, Notes and Records Roy. Soc. London 44 (1) (1990), 13-23.
  6. J Marek, Les notions de la théorie ondulatoire de la lumière chez Grimaldi et Huyghens, Acta historiae rerum naturalium necnon technicarum I (1965), 131-147.
  7. J Marek, The Role of Practice in Marxism-Leninism: The Idea of Limits as Impetus in the Development of 17th-Century Physics, Studies in Soviet Thought 25 (1) (1983), 1-10.
  8. R H Stuewer, A Critical Analysis of Newton's Work on Diffraction, Isis 61 (1970), 188-205.

 




الجبر أحد الفروع الرئيسية في الرياضيات، حيث إن التمكن من الرياضيات يعتمد على الفهم السليم للجبر. ويستخدم المهندسون والعلماء الجبر يومياً، وتعول المشاريع التجارية والصناعية على الجبر لحل الكثير من المعضلات التي تتعرض لها. ونظراً لأهمية الجبر في الحياة العصرية فإنه يدرّس في المدارس والجامعات في جميع أنحاء العالم. ويُعجب الكثير من الدارسين للجبر بقدرته وفائدته الكبيرتين، إذ باستخدام الجبر يمكن للمرء أن يحل كثيرًا من المسائل التي يتعذر حلها باستخدام الحساب فقط.وجاء اسمه من كتاب عالم الرياضيات والفلك والرحالة محمد بن موسى الخورازمي.


يعتبر علم المثلثات Trigonometry علماً عربياً ، فرياضيو العرب فضلوا علم المثلثات عن علم الفلك كأنهما علمين متداخلين ، ونظموه تنظيماً فيه لكثير من الدقة ، وقد كان اليونان يستعملون وتر CORDE ضعف القوسي قياس الزوايا ، فاستعاض رياضيو العرب عن الوتر بالجيب SINUS فأنت هذه الاستعاضة إلى تسهيل كثير من الاعمال الرياضية.

تعتبر المعادلات التفاضلية خير وسيلة لوصف معظم المـسائل الهندسـية والرياضـية والعلمية على حد سواء، إذ يتضح ذلك جليا في وصف عمليات انتقال الحرارة، جريان الموائـع، الحركة الموجية، الدوائر الإلكترونية فضلاً عن استخدامها في مسائل الهياكل الإنشائية والوصف الرياضي للتفاعلات الكيميائية.
ففي في الرياضيات, يطلق اسم المعادلات التفاضلية على المعادلات التي تحوي مشتقات و تفاضلات لبعض الدوال الرياضية و تظهر فيها بشكل متغيرات المعادلة . و يكون الهدف من حل هذه المعادلات هو إيجاد هذه الدوال الرياضية التي تحقق مشتقات هذه المعادلات.