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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


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!]


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.





Veritas Press Teacher Training 2018

I am pleased to announce that I will return to beautiful Lancaster, Pennsylvania this summer to speak at the annual Veritas Press Teacher Training Conference on July 11- 13. If you attended last year, you may recall that I walked through best practices in teaching through Latin for Children, Latin Alive Book 1, and Wheelock.  This year I will be taking on some different topics, though still related to these same ages and stages. (If you missed the 2017 conference you can get my Latin sessions through Veritas Press).

Here is a sneak peek at the topics I am speaking on this year!

Latin: The Key to the Grammar School

Latin is often considered a core element to a classical education, even in the younger years of grammar school. This session will explore the reasons why Latin is a key component in the grammar years and how this study can support and reinforce other subjects. Topics covered will include vocabulary, grammar, enrichment, and integrative opportunities with other subjects.

Latin: Taking it Beyond Vocabulary

This second session will build on the vocabulary skills introduced in session one. The goal of teaching Latin is to be able to read wonderful stories written in this ancient and beautiful language. In this session the class will move beyond vocabulary to consider how students can apply words to simple sentences, eventually reading simple stories. This class will use lessons within the Latin for Children series along with stories from the Libellus de Historia Reader series to demonstrate how to teach students to read Latin.

Latin I for All Children

As enrollment grows and new students join existing schools and programs, how do we bring new students into our Latin programs? This seminar will explore ways to welcome new students and set them up for success in classical languages. We will look at entry points for grammar, logic, and rhetoric programs. We will also consider opportunities for additional support as students adapt and grow.

Using Latin Alive!

As students mature their styles of learning change, and so must our style of teaching. The paradigms are the same, but we must move beyond them to find ways to make Latin come alive for our students. This session will highlight teaching strategies for older students utilizing some of the lessons and tools of the Latin Alive program. Karen Moore, Latin teacher and author of Latin Alive, will also share a number of techniques she has developed as we review the finer points of Latin grammar, reading, and even a little composition.


For more information on the Veritas Teacher Training Conference, including registration visit


Latin Practicum @ ACCS with Karen Moore and Tim Griffith

I am very excited to partner with Tim Griffith in bringing a full day of Latin wonder to the pre-conference for the 2018 Repairing the Ruins Conference, hosted by the Association of Classical Christian Schools. My distinguished colleague is a professor of classical studies at New St. Andrews College and the brilliant creator of Picta Dicta (click to see my earlier post extolling this site!). I have enjoyed getting to know him over the last year as we exchanged ideas and shared our passion for Latin. Our goal as we join forces is to bring together teachers from a variety of disciplines, approaches, and backgrounds to discuss "best practices" for the various ages and stages of learning. Every teacher has their own strengths, weaknesses, and preferences. Likewise, our students all have various approaches to learning. The goal is to find the best ways to engage students in a variety of approaches to strengthen not only their skill sets in language, but their love for learning. Tim and I will also share a wide variety of resources for use inside the classroom as well as for teacher development outside the classroom. Read the rest of this entry »

Gingerbread Construction – Recipes and Tips

On this blog site I have posted multiple projects that teach lessons in ancient architecture via gingerbread. This particular post will offer a "behind the scenes" look at the construction process. Read on for information on creative tools, gingerbread and icing recipes, and a variety of construction tips. Caveat: this post will make you hungry! Read the rest of this entry »

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 »

Columbus Day Reading: Integrating History, Language, and Science

Each October my 9th grade students enjoy reading selections from the Latin Letter of Columbus. Columbus addressed his to the monarchs of Spain, King Ferdinand and Queen Isabella, and thus he originally wrote the letter in Spanish. The monarchs were delighted by the discovery and immediately wanted to share news of this new world with all of Europe. Therefore, in 1493 they  published Columbus' letter in Latin, and sent it throughout all of Europe. At that time Latin was the lingua franca of the day, and every well-educated man, woman, and child would be able to read these great tidings. This leaves us a wonderful sample of Renaissance Latin about historical places and events on our side of the pond. Read on to learn how I use this letter to integrate the study of Latin with American History and how this provides the basis for a creative composition assignment! Read the rest of this entry »

Latin Authors in Italy: A Study Tour for Teachers

This summer I was afforded the great blessing of attending Latin Authors in Italy, a study tour designed specifically for high school Latin teachers. The title and description resonated with me immediately. Here I was promised the opportunity to read Latin authors in situ, to walk through the remains of Ancient Rome with an experienced archaeologist, and to discuss practical pedagogical applications with an experienced high school Latin teacher. The balance of culture, history, art, and literature described seemed almost too good to be true. The experience did not disappoint, on the contrary it exceeded my every expectation. Read on for my full review of the summer study program every Latin teacher dreams of (or should). Read the rest of this entry »

Vocabulary Building with Picta Dicta

Picta Dicta is an innovative and highly engaging tool for students to build their Latin vocabulary. This program could easily serve as an introduction for young students into the delightful world of Latin. The lessons would also prove a wonderful supplement to any Latin curricula, or even as a summer strengthening program for Latin students. The approach engages students in learning vocabulary through pictures and images rather than the usual vocab word list found in most textbooks. 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 »

Rainbow Resource: Review of Latin Alive Book 1

The following review of the Latin Alive series is posted on Rainbow Resource Center.

Maybe you just recently decided to incorporate Latin into your homeschool, and you’re looking over your shoulder at the fun and simple elementary programs that are now too basic and ahead at the thick and intimidating upper-level courses available. You wonder, “Can my child really handle that?” If you’re wanting to begin now, never fear! This well-designed and manageable course by Classical Academic Press is designed for middle school and high-school students who are just starting out in Latin. The series, which will eventually consist of three books which make up a 3-year program, provides students the opportunity to learn the Latin language and grammar, using an incremental approach. Drawing upon the successful teaching methodology used in Wheelock’s Latin, the authors of this program have in essence taken the best approaches and features of Wheelock’s, and designed a thorough course that is more appropriate (and exciting) for middle school and high school beginners. Also, because the novelty of studying Latin only goes so far, the program also does a fantastic job of demonstrating how relevant Latin is to us, even today. If you are not just starting out in Latin, or perhaps even wanting to continue your journey from Latin for Children, you will find much review in Book One, but thorough coverage of grammar and the reading passages from Latin writers will be well worth continuing your journey.

For the full review, which includes a thorough description of the book click here.