The Elements of Euclid in Greek and Latin

I was trying to parse my way through an edition of The Elements in Greek and Latin:

https://archive.org/details/euclidisoperaomn01eucluoft/page/x

The name of The Elements in Ancient Greek is:

Στοιχει̃a

or, when transliterated:

Stoicheĩa

.

The Ancient-Greek word, τὰ στοιχει̃α or, when transliterated ‘tà stoicheĩa,’ is a plural form of the 2nd-declension neuter verb, τὸ στοιχει̃ον genitive: του̃ στοιχείου or, when transliterated: ‘tò stoicheĩon,’ genitive: ‘toũ stoicheíou.’

The Ancient-Greek word, ‘tò stoicheĩon,’ can mean ‘an element in a set.’

Figure 1: The elements of this set are alpha, beta, gamma and delta.

The Ancient-Greek word, ‘tò stoicheĩon,’ is formed from the Ancient-Greek masculine noun, ὁ στοι̃χος genitive: του̃ στοίχου or, when transliterated, ‘ho stoĩchos,’ genitive: ‘toũ stoíchou,’ which means ‘steps,’ or ‘a flight of stairs;’ and the Ancient-Greek 2nd-declension neuter nominal suffix, ‘-eĩon,’ genitive: ‘-eíou’ which denotes ‘a means (of),’ ‘an instrument of;’ etc.

Figure 2: a ‘stoĩchos’ or ‘series of steps.’

The term, ‘stoĩchos,’ according to Wiktionary, may be traced back to the indo-european word:

*steigʰ

, which means:

‘climb.’

Hence, etymologically, the Ancient-Greek term, ‘stoicheĩa,’ can be said to mean: ‘the means of climbing up;’ ‘the means of stepping up;’ ‘the means of ascent;’ etc.

This is highly instructive, as, in truth, Elements is a book that is a Jacob’s ladder, of sorts, by which one can ascend, element by element, into the heavens of mathematical knowledge.

Figure 3: With The Elements of Euclid, we advance in our mathematical knowledge element by element. Each element is, conceptually, like a rung, heaving us upwards to Mathematical prowess; to an implicit knowledge of Euclidean Geometry.

The Straight Edge:

The better that I know plane and cartesian Geometry, the better that I can both script, and draw (using a free open-source suite like Inkscape) computer Graphics.

In Plane Geometry, a straight edge is used.  A straight edge differs from a ruler, in that:

• whereas rulers possess gradated markings that indicate standard units of measurement, there are no gradated markings that indicate standard units of measurement – such as millimeters centimeters, etc. – on a straight edge.
• the width of the straight edge is deemed infinite, whereas real-life rulers are, it is needless to say, of finite width.

Figure 1:  A collapsible compass and straight edge.  These two instruments are employed in the construction of figures in Euclidean Geometry.  The span of a collapsible compass is deemed to collapse, should both the metallic point, and the graphite point of the compass be removed at the same time from the page.

See the Pen Collapsible Compass and Straight Edge Inkscape SVG by Ciaran Mc Ardle (@Valerius_de_Hib) on CodePen.

 

Anatomy for Artists: How to Draw the Shoulder.

Anatomy for Artists pdf

The above links to a pdf version of this blog post.

I hope, one day, in the dim and distant future, to become a great artist.

“LADY MACBETH:..To beguile the time, look like the time…”

In Act I Scene V of The Tragedy of Macbeth, Lady Macbeth tells Macbeth that so as to triumph in the present age, one must – at the very least – pretend to possess the sensibilities of the present age. To paraphrase another Shakespeare play:

“Deviousness, thy name is woman![1]”

Whereas Lady Macbeth said that to triumph over the age, we must imitate the age, it follows that to become great in a field, one must imitate the greats of that field.

So it goes with art. The Artists of the Renaissance tried to incorporate the Geometry of Euclid into their Art. Filippo Brunrlleschi (1377 – 1446) the architect who designed the dome of Florence Cathedral did this, and his contemporary, Leon Battista Alberti (1404 – 1472) wrote a book on this topic, De Pictura, which I am trying to read at the minute.

I, also, am reading up on Geometry, and attempting to find a way so as to incorporate it into my art.

Other Renaissance Artists, such as Leonardo Da Vinci, (1452 – 1592) were as much physicians as they were painters and sculptors. Leonardo Da Vinci had a diary – written in mirrored-coded script – in which he was ever recording anatomical observations.

My anatomical knowledge is extremely poor, but I am hoping to alter this fact.

I have bought a book, Human Anatomy: The Definitive Guide[2], and have begun to sketch copies of some of its illustrations.

Figure 1: The Shoulder. I drew this with pencils.

Figure 2: I used Microsoft Paint so as to label the various bones that I hand drew.

1. Clavicle. The technical name for ‘Collarbone.’ It is the only long bone in the body that lies horizontally. The term ‘clavicle’ is derived from the Latin feminine noun, ‘clāvicula, clāviculæ,’ meaning ‘small key.’ Ultimately derived from the Latin feminine noun, ‘clāvis, clāvis,’ key.
2. Scapula. The technical name for ‘Shoulder Blade.’ In medieval times, there existed an article of clothing called a ‘scapular,’[3] so called as it was a piece of cloth worn between the shoulder blades.
3. Acromion. From the Ancient-Greek ‘ákros’ meaning ‘topmost,’ and the Ancient-Greek masculine noun ‘ho ȭmos,’ ‘the shoulder.’

“a bony projection from the outer end of the spine of the shoulder blade, to which the collarbone is attached”

[4]”

• Humerus.

“noun. [ANATOMY] the bone of the upper arm or forelimb forming joints at the shoulder and the elbow.[5]”

As mentioned above, the humerus forms the elbow joint with the radius and the ulna. When this joint gets a bash, a funnily painful sensation results. Hence its name “the funny bone.” The similarity in spelling between ‘humerus’ and the adjective ‘humorous’ is to be noted. ‘Humerus’ and ‘humorous’ are largely homophonic[6]. ‘Humorous’ and ‘funny’ are synonyms, and I believe that this is why the joint formed by the humerus is called ‘the funny bone.’

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[1] “HAMLET: Frailty, thy Name is Woman.” Hamlet: The Prince of Denmark Act I Scene II. William Shakespeare.

[2] DK. London. (2014).

[3] From the Latin 3^rd-declension adjective, ‘scapulāris, scapulāre,’ which means ‘pertaining to the shoulder blade.’

[4] Encarta Dictionary.

[5] Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010. Loc 336066.

[6] Adjective. Describing two – or more – words that are pronounced identically. From the Ancient-Greek adjective ‘homos,’ ‘the same,’ and the Ancient-Greek noun,’ ‘phōnḗ,’ which means ‘sound.’ The etymological sense of ‘homophonic’ is ‘words that have the same sound as one another.’