How was the first carpenter's square made?
score:3
Proposition 11 of Book I of Euclid's Elements (circa 300 B.C. in Alexandria Egypt) is:
To draw a straight line at right angles to a given straight line from a given point on it.
Note that Euclid's contribution to geometry is one of compilation, and of constructing a formal axiomatic system for plane geometry. Most if not all the work was well known long before Euclid, and for the early propositions of Book I this "prior time period" measures in centuries if not millennia. The first square is thus so far back in antiquity as to be most likely impossible to date.
It is certainly true that the ancient Egyptians were quite able to construct right angles well before the construction of the earliest pyramids, and most likely were also aware of the Pythagorean triple (3,4,5).
First Propositions of Book I
The Babylonian clay table known as Plimpton 322, from about 1800 B.C.E., contains a list of Pythagorean Triples:
In each row, the number in the second column can be interpreted as the shorter side s of a right triangle, and the number in the third column can be interpreted as the hypotenuse d of the triangle. In all cases, the longer side l is also an integer, making s and d two elements of a Pythagorean triple
Upvote:1
How can someone create a right angle tool "from scratch"?
Mathematics
If you can create a straight edge, you can construct a square. You don't need to know any trigonometry beyond the idea that two right-angles make a straight line.
1. Produce a straight edge
Generally, to the level of accuracy needed for woodworking (joinery etc) you can tell whether an edge is straight by looking along it with your unaided eye. You can construct tools such as long wooden "jointer" planes that aid in the production of straight edges on planks but the general technique is not dependent on having a straight tool already. If your eyesight isn't good enough you lay your straight edge on another flattish plank and draw a line using the straight edge, then you rotate the straight edge 180, align its ends to the first line and draw a second line over the first. If the edge isn't straight the two lines will visibly diverge at one or more places in between the aligned ends.
This is a simpler case than creating a perfectly flat two dimensional surface of the sort that precision machinists use to check their work and their tools. A typical high-precision granite surface plate is flattened by nothing more complex than rubbing two lumps of granite together. Quickly measuring the flatness to high accuracy may require precision optics but this isn't really a task that requires powered machinery or electronics. It doesn't require a reference surface.
2. Use the straight edge to produce a square.
You can then create an L-shaped "square" by eye and check it against your straight edge. The method is to lay one arm of your square against the straight edge of a plank and mark a first perpendicular line across the plank along the other edge of the square, you then flip the square over, align the square where the line meets the straight-edge and draw a second perpendicular line across the plank, this will likely form a narrow V because your square is not exactly right. You can see how far out your square is and make appropriate adjustments, repeating the process until you are no longer able to see any divergence in your perpendiculars.
Notes
Current day carpenters and machinists routinely use these methods to check squares.
More post
- 📝 How to identify this coin with a bust on one side and the letters S and C on the other side?
- 📝 How much did J. Robert Oppenheimer get paid while overseeing the Manhattan Project?
- 📝 Has the American Civil War led to any significant innovations in 19th-century warfare?
- 📝 Did the "I have a dream" speech make a big impact at the time it was spoken?
- 📝 What evidence is there to suggest that 'fear of the bomb' is culturally specific?
- 📝 Quantitative comparison of transportation cost per kilometer over the centuries?
- 📝 During Iranian Hostage Crisis, were shredded documents reassembled by children?
- 📝 Who should be the king/queen of England?
- 📝 Gregorian dating in the Julian time period?
- 📝 What were the typical types of ships used in the Persian Navy in the 1730's and 1740's?
- 📝 Early reasons to bury the dead
- 📝 Did either of the World Wars involve South or Central America?
- 📝 What do we know of the conditions the "prominents" were kept in in Nazi concentration camps?
- 📝 Where can I find more information on the Katyn massacre?
- 📝 Why and how did some Germans choose to join the Stasi (Staatssicherheit)?
- 📝 Were the Puritans for a State Church?
- 📝 Why was Charles I not pressed by *peine forte et dure* to force him to plead to treason in front of the High Court?
- 📝 Was there car insurance in the USSR?
- 📝 Why did the Romans incorporate and rename the Greek pantheon?
- 📝 The Battle of Britain
- 📝 Income versus living expense in USSR during the 1980's and 1990's
- 📝 How often were slaves raised by their parents in 19th century USA?
- 📝 How was the Urnfield culture represented around 1300 BC in the area the Romans called Gallia Belgica?
- 📝 How to find the population and mortality in London during the period 1760-1834?
- 📝 How do historians and linguists know how to pronounce the names from non-phonetic scripts?
- 📝 In which banking institute was Soren Kierkegaard a customer?
- 📝 How and when was Portugal created?
- 📝 What was at the start of Early Roman codices?
- 📝 What's the history of this mortar shell?
- 📝 Which company offered this aircraft interior in the 60s?
Source: stackoverflow.com
Search Posts
Related post
- 📝 How was the first carpenter's square made?
- 📝 How common was smoking in first half of the 20th century?
- 📝 In the first half of 20th century, how was gold inspected for authenticity?
- 📝 How was the first official geographical border established in Europe?
- 📝 How was whiskey made in the 1800's?
- 📝 How long ago was the yo-yo first used as a weapon?
- 📝 In the First Barbary War, how long was the USS Philadelphia aground?
- 📝 Who was the first woman to be made a god by Rome's senate?
- 📝 How can we be sure what the first day of the month was 2000 years ago and how can we determine which years were leap years?
- 📝 Is there any evidence to support the claim that the United States was "suckered into WW1" by Zionists, made by Benjamin Freedman in his 1961 speech?
- 📝 How serious was Fermat's statement about the ancients?
- 📝 How and when was the modern company ownership structure invented?
- 📝 How was the United States able to produce excellent tanks in 1942?
- 📝 Who, if anyone, was the first astronaut to return to earth in a different vessel?
- 📝 What was the first solar eclipse that was demonstrably predicted in advance?
- 📝 When did the term "Nationality" first come into use? How did ancient civilizations refer to themselves? By ethnicity?
- 📝 Which religion was the first monotheistic one?
- 📝 How did people react to Cavendish bananas when they first replaced the Gros Michel strain?
- 📝 Who was the first female ruler to be given the suffix, "the great"?
- 📝 How popular was the Soviet Union?
- 📝 How difficult was to escape from a naval battle after engaging into one during the Age of Sail?
- 📝 How likely is it that any non-Celtic language was spoken in the British Isles when the Romans invaded?
- 📝 How significant was the Fall of Constantinople as an event leading to the Age of Exploration?
- 📝 What was the first battle in history fought by vast-majority-% "distance-shooting" non-mechanized force?
- 📝 What / When was the first use of concentration camps in history?
- 📝 How and why was the boundary between West and East Berlin decided to be where it was?
- 📝 How difficult was it to spoof the sender of a telegram in 1890-1920's in USA?
- 📝 How was the modern geographic boundary between Europe and Asia decided?
- 📝 When and where were the first coins made showing the currency or a face value?
- 📝 How was the Luftwaffe able to destroy nearly 4000 Soviet aircraft in 3 days of operation Barbarossa?