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Lesson Plans and Ideas

Newton’s Prinicipia: a lesson in Latin and Science

Once I asked my good friend Ravi Jain if I were to include a Latin reading from a math/science source in my reader, what would he advise. Ravi is a math-science teacher at the Geneva School in Orlando. He is also the co-author of The Liberal Arts Tradition: A Philosophy of Christian Classical EducationRavi is very well versed in subjects on math, science, philosophy, theology, and even a bit of language. Moreover, he is a wonderfully engaging teacher, and thus the perfect person to direct me to the best resources to mine gems on Latin and science. When I asked Ravi for his recommendation on a Latin piece by which to study science his immediate response was Isaac Newton’s Philosophiae Naturalis Principia Mathematica. 

This work, originally published on July 5, 1687, has since been considered one of the most important works in the history of science. It is in this work that Newton sets forth the laws of motion, which form the foundation of classical mechanics; the universal law of gravitation; and a derivation of Kepler’s laws of planetary motion. Full copies of the original work can be found in Latin or various translations online. On Ravi’s advice, I chose passages covering the three laws of motion for the Latin Alive Reader; for this classical set of laws is well known to most students even if they have not yet studied physics. The rest of this post will be dedicated to how I teach Newton’s laws of motion via Latin or teach Latin via Newton’s laws. Whichever way one chooses to look at it.

 

Reading the Principia:

Caveat Magister: The Principia will not “read” like most Latin texts read in class, and may even differ from all those you have read in most teachers’ own training. This work is neither poetry nor prose, but it is a scientific treatise. The frame work consists of the three leges [laws], each followed by a scholia [lesson] that expounds upon the law. The laws themselves must be read as extended forms of indirect discourse without a proper introductory statement.  For example, normal indirect discourse would read something like:

Lex dicit objectum actioni contrarium semper & aequalem esse reactionem

The main clause, if you will, would be Lex dicit [The law says]. The indirect discourse would be the remainder of the sentence or what the law says. The verb within the indirect discourse is always an infinitive that we would render in English as an indicative verb: actioni contrarium semper & aequalem esse reactionem [for an action there is always an opposite and equal reaction].

Newton, however, foregoes the main clause as he states each law. He just lists the three laws of motion with infinitive vebs in lieu of indicative verbs as is read in indirect discourse.

Actioni contrarium semper & aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales & in partes contrarias dirigi.

Teachers will want to point this out to the students before beginining any reading of the Prinicipia as this unfamiliar format may throw them off. I find that once I explain the structure and advise them to pretend or assume the phrase lex dicit before each law, the students flow along with the reading of the laws themselves very well.

The scholia that follows each law is more or less in a form of prose that is easy to follow. Newton does like to use the ampersand in place of et (as seen in the above example). The scholia will give an expanded explanation of the law and provide examples of the law in form. These provide great material for class discussion (in English or in Latin) on the laws and the Latin text. I usually like to end the study with some composition assignments as will be seen below.

General Lesson Plan:

  1. Ask the students to create an “unfamiliar vocabulary list.”

Before reading or translating, ask the students to create a list of all the Latin words they do not immediately recognize. This will help warm their minds to the reading and topics to be considered. This will also make your time reading flow more smoothly as it provides a reference aide and prevents the frustrating stop-start-stop-start pattern of reading as students fumble to look up words. The exercise will also lead students to recognize the high level of English derivatives in Latin during the 17th century.

When making an unfamiliar vocab list I generally ask students to write down the genitive singular and gender for nouns and the principle parts of verbs. This also allows for discussion on appropirate agreement, tense, syntax, etc. as we read. It is wise for students to also write down more than one meaning as sometimes the meaning most applicable to our context might not be the first word listed in the dictionary.

2. Reading the laws themselves

There are two approaches I generally follow for reading. The first is a prepared translation, meaning that students work through a written translation prior to a class reading and discussion. The second is a sight reading. With Newton’s passage I generally prefer a sight read, so that is the process I will provide here. IF you do prefer to assign students the task of translating the passage prior to the class reading, please please please do NOT allow them to read off their English translations during discussion time. Such time should be devoted to reading from the Latin text, not their English work.

A) Ask a student to read a portion of the Latin text in Latin. You may choose to have them read a clause or a phrase or an entire sentence. I sometimes, as the teacher, will read the entire law myself first to model pronunciation, particularly since some of these words are new. However, it is very important for the students to read out loud and to hear themselves and their classmates reading the language out loud.

B) Check for general understanding. Before someone renders an English interpretation of the phrase, discuss in general what is being discussed or happening. This does not necessitate taking every single word into account. If there is a word that is unfamiliar or unknown – skip it. Don’t let the words they don’t know rob them of what they do know. Use what they recognize and the context to get at the general meaning. This can be done in English or in Latin or in both languages.

C) Ask a student to interpret the phrase or sentence into English. This can be intimidating for some, so make sure to give praise for everything that is correct. If the student interprets the general sense correctly but errs in some grammatical particulars such as the number of a noun or the tense of a verb or skips over a word, I will praise the student for understanding the sentence. Then I will go back to “clean up grammar” but make sure the class (and student especially) understand we are doing that as an opportunity to review and understand the grammar. It is very important that students understand they can still read a passage and understand a reading even without 100% accuracy on vocabulary and grammar. After all, how many times do they understand Shakespeare’s English 100%?

D) At the end of a section, take time to recap or review what Newton has stated or is trying to explain. Once again this can be done in Latin or in English. Either way, you are now integrating physics and Latin!!!

See Step 3 Below on Class Discussion

E) I often will conclude these lessons by asking students to turn in a written translation. However, there are other ways to assess understanding of a passage and I used them abundantly!

3. Class Discussion

Content

As we read through the passage together in Latin, I like to take the opportunity to discuss what we are reading. Go beyond just translating what each word or sentence means, and explore what Newton is trying to teach us via the examples he is giving. Some of these discussions can take place via oral Latin conversation. Some might need to use English to explore the concepts of physics.  For example, in his third law Newton uses the example of a finger pressing on a stone in order to explain the third law of motion – for an action there is always an opposite and equal reaction.  Newton writes:

Quicquid premit vel trahit alterum, tantundem ab eo premitur vel trahitur. Si quis lapidem digito premit, premitur & huius digitus a lapide.

Newton is trying to demonstrate that while the finger is pressing the stone, the stone is also pressing back on the finger with an “opposite and equal reaction.”  Bring a stone to class to demonstrate. Or even a class set of stones. Then ask questions such as the following.

Omnes, premite lapidem tuum. Quid premitis? [ lapidem]. Quid digitus tuus premit? [lapidem] Quid lapis premit? [digitum] Quid ab lapide premitur? [digitus] Quid ab digito premitur? [lapis]

Estne reactio et contraria et aequalis actioni? [Ita vero!]

Style

Also take time to discuss Newton’s style of writing. He makes some intentional word choices in terms of both vocabulary and arrangement. For example, note that he uses both the verbs premit and trahit in that first sentence. This is the sentence that both follows the third law of motion (seen above) and introduces the scholia demonstrating the third law. Why does he use both of these particular verbs?  Note that premit is then used in the example of the stone. The lines that follow (not shown here) go on to use the example of a horse dragging (trahit) a rock tied with a rope.  Thus, these two verbs are chosen as they apply directly to the examples Newton will give.  Also note that in the second sentence Newton juxtaposes the words premit and premitur. He is using a rhetorical device called anadiplosis to place particular emphasis not only on this action, but on the change from active to passive in the example of this action. Brilliant!

4. Composition

As has been pointed out, each scholia follows the statement of each lex. The scholia usually provides at least one example of the law in action such as the trundling hoop or the horse with the rope and the rock. Ask students to compose their own original scholia in Latin to demonstrate one of the three laws of motion. I usually assign the topic of a baseball being hit by a bat. Before composing we discuss how this action reflects each of Newton’s laws, how this example might resemble those Newton has already given, and what parts of Newton’s writing specifically might be applied to such a scholia. Require that the students begin their composition by restating Newton’s law. Encourage them to use Newton’s vocabulary and imitate his style as much as possible.

I usually have the students turn in a rough draft to which I make edits. I advise them on corrections needed without giving the answers. For example, I might write that a tense or a case needs to be changed. Or, I might suggest that they pay attention to noun-verb or noun-adjective agreement in a certain sentence. I want to guide my young scientists in the right direction without doing the work for them. After the final copies are turned in, send an email to parent to praise the physics lesson and the scientific compositions the students created in Latin class! This is a lesson sure to encourage both your students and their parents in the value of Latin in the world of science.

 

 

 

 

Edible Architecture: Hadrian’s Wall

Among the most creative of our edible construction projects was Hadrian's Wall. This project was very unique, very different from other projects of its kind. First, instead of recreating a finished structure, we opted to recreate the structure in process. Second, this project did not use any gingerbread. However, like all of our other edible architecture projects we did recreate a structure that was significant to the classical world, and every piece was edible. Read on to learn a little history behind the real wall, and then how to build your own sweet replica. Read the rest of this entry »

Art-Literature Analysis: Student Assignment

As an end of year project for my AP Latin students, I assign an art analysis paper based upon a scene from either Vergil's Aeneid or Caesar's de Bello Gallico. The students are to choose a masterpiece that accurately depicts one such scene. This assignment is a student favorite as it causes the students to look back and call upon what they have learned of the story and the language from the vantage point of one who has completed a rigorous journey and now stands upon the mountain top, surveying the view of the road from whence they came. The remainder of this post is written by one of my Latin students. This is her piece of art-literature analysis based on a scene from Aeneid VI. Read the rest of this entry »

Composition Assignment: Classic Narratives

Our 3rd grade grammar school students love that first special moment that they are able to read a story in Latin for themselves. This is a huge milestone. Their eyes just light up with the realization that they are truly comprehending a story in another language. From that moment on, Latin stories become a favorite class activity. Another great milestone comes at the end of 5th grade when they are then able to compose a story in Latin for others to read. Up until this moment they have received the joyful gift of reading, now they are able to give that gift in return. This post outlines our grammar school composition project. Read the rest of this entry »

Planning the Invasion of Gaul

Gallia est omnis divisa in partes tres . . . Thus begins the first chapter of Comentarii de Bello Galllico, written by General Julius Caesar c.58-49 B.C. This is a line that most veterans of Latin studies know by heart for it has long been the traditional "first book" for young students graduating from grammatical studies into original readings. The work is chosen for its excellent prose, whose arrangment is fairly easy for novice readers to follow. That is once you become adept at recognizing ablative absolutes and extensive relative clauses and very long stints of indirect discourse. The work certainly cannot be read without great attention to the author, Julius Caesar, his military endeavors and his political ambitions. This work can also be enjoyed as a study in ancient geography as Caesar begins the very first chapter by laying out the geographical composition of Greater Gaul in the manner of a chartographer. Read the rest of this entry »

Gingerbread Pantheon

Augustus was said to have found Rome a city of brick and left it a city of marble. Our Classics Club at Grace Academy is rebuilding Rome as a city of gingerbread! Each year our students take on the task of rebuilding a significant piece of ancient architecture from gingerbread and other edible materials. This year our group took on the Roman Pantheon. We entered the finished piece in the Georgetown Library's annual Edible Extravaganza contest where it won first place in its division. This post shares some of the secrets behind the triumph. Read the rest of this entry »

Imitation in Writing through Latin

l believe the purpose of learning the Latin language is in order to study Latin literature. By studying Latin literature, I mean studying the Great Books. These are great pieces of literature of outstanding merit that have stood the test of time. Such works reflect the worldview of the culture and time in which they were written. Such works have often influenced not only the people of their own time, but the people of times that would follow. Such works should demonstrate some combination of Truth, Beauty, and Goodness. By studying such works we better understand the flow of human thought over the course of history. We better understand our civilization when we know from whence it came. We better understand what is truly great literature. By studying Latin literature, I mean Read the rest of this entry »

Latin Composition: Thanksgiving Theses

The philosopher Seneca is quoted as saying "docendo discimus" [by teaching we learn]. The idea behind this statement is that one must learn something really well in order to turn around and produce that learning for someone else. We teachers could also say "linguam scribendo discimus" [by writing we learn language]. I love for students to practice the grammar and vocabulary they have learned by reading authentic Latin literature. We can take these lessons a step further by challenging students to practice these same tools by producing a composition that imitates the literary works they read. These are two very different disciplines that engage the students in language from two different angles. Such assignments allow them to Read the rest of this entry »

Language Tree Project

The Latin Family Tree is a beautiful creation. Its roots run deep into the Proto-Indo-European language spoken through most of Europe c.5,000 B.C. Its trunk reveals beautiful hues of Italic languages influenced by the Etruscans and the Greeks. Its lofty branches reach far and strong to provide the arboreal beauty of modern Romance languages: Italian, Spanish, French, Romanian, and Portuguese. What delight to play in its shade and admire its beauty! Chapter 5 of Latin for Children, Primer A offers young students a peek at the Latin Family Tree. Our third grade class at Grace Academy engages in this study through this simple yet delightful two-day project. Read the rest of this entry »

Poetic Art Assignment

In a recent post (July 5) I discussed my love for exploring the connections between Latin poetry and art in my classes.

Within that post I shared suggestions for a class lesson that would integrate the analysis of poetic imagery with pieces of art.  In such lessons we must begin with the work of master artists.  We learn what is truly beautiful by studying the work of those who have mastered the art form, whether that be in the visual arts or in the literary arts.  The next step in the art-poetry study is for the students themselves to become creative interpreters of the poem.  In my last post we looked at the story of Pyramus & Thisbe from Ovid’s Metamorphoses (Liber IV).  So let us continue with that same story in our next art lesson.

We begin by reading the story in the original Latin and soaking up the masterful wordcraft of the poet Ovid.  We discuss word choice, arrangement, imagery, and all sorts of literary devices.  We next look at works by master artists to see how they interpreted Ovid’s poem upon their canvases.  We discuss the art in light of the poetry (see July 5 post for guidelines).  Next, I assign the students the task of producing their own piece of art that interprets one scene one moment from the poem.  After looking upon the work of masterful artists this naturally causes a bit of intimidation.  I comfort the students by assuring them that I don’t expect a masterpiece.  I do expect their best work, careful, neat, thoughtful, with attention to the detail in the poem.   I am pleased to share the work of one of my freshmen ladies below.  This is her interpretation of Book IV, Line 71:

saepe, ubi constiterant hinc Thisbe, Pyramus illinc

Kirk_Ovid_05_2016

 

What I absolutely love about this particular piece is the manner in which she interprets the chiastic imagery from Ovid’s work.  A chiasmus is an ABBA word pattern.  Here the word arrangement highlights the tortuous juxtaposition of the two lovers separated by the wall.  The wall itself becomes an impersonal character within the story.  Later on the young lovers would talk to the wall both chastising it for their separation while also expressing gratitude for the crack (seen here above Pyramus’ head) that allows them to share secret whispers of gentle affection.  The astute observer may notice that the artist did change one word from Ovid’s verse.  The artist writes semper [always] where Ovid wrote saepe [often].  This is and intentional change.  The artist has chosen silhouettes to illustrate the spirit that remains for these young lovers – always and forever juxtaposed against the wall in Ovid’s story. Many other pieces I receive have used the death scene (my students seem to love gore) and include a greater multitude of details. This piece, however, was bold enough in its abstract simplicity to drive home the image of the wall and the manner in which it divided the two lovers, here Thisbe, Pyramus there – always.

Well done, my young poetic artist!