Submitted by Hairy Scot  •  November 29, 2011

Perpendicular

When did perpendicular lose its verticality? I have always understood perpendicular as being “at right angles to the plane of the horizon” ie: at right angles and vertical.

OED:- 1. perpendicular, adj. and n. ...Situated or directed at right angles to the plane of the horizon; vertical....

The wall is at perpendicular to the floor but the floor is at right angles to the wall.

But more and more I hear it being used as meaning at right angles regardless of the plane. I have even seen such a reference in print. Once again our good friend Jeffrey Deaver:- “I took a chair perpendicular to his.” Another example of evolution?

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@Ing
I do not dispute any of the definitions you provide.
The OED and Chambers provide the same definitions.
Geometric or engineering documents depict 3 dimensions on a 2 dimensional plane so there is a valid reason for the use of perpendicular in those cases since a number of the lines on the document would represent lines that would be vertical in real life.
If most people say "upright" or "vertical" in preference to "perpendicular" then why would anyone say something like "I took a chair perpendicular to his" instead of "I took a chair".
Perhaps this is the result of someone who, trying to be clever, ends up using a word wrongly or out of context. I have seen similar cases with mathematical terms such as "orthogonal".
"Perpendicular comes from the Latin verb "pendere" which means to hang.

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I may be an English nazi with my friends, but math has always been my favorite subject ;) Thus, I use the word 'perpendicular' to mean anything at a right angle to the object I'm describing.
I would think 'plumb' is equally suitable to your task, and probably more widely recognized as being reserved for 'perpendicular to the horizon'.

A somewhat interesting thought occurred to me just now. If two walls are to be truly perpendicular in the sense of your favored meaning of the word, then they cannot be parallel to each other, for the earth is round, and the horizon from each point would be slightly different (that is, if we can use the idea that another way to explain perpendicular would be to say that it must coincide with a radial line directly from the center of the Earth). Sorry, rambling ;)

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'A pedantic old curmudgeon' eh? ;) Nice! Wouldn't that make everyone else the curmudgeons if you're the pedantic?

Well - in learning more about physics and all - when flying, apparently the shortest distance is not a straight line. Go figure :P

I can understand and respect your holding on. I do the same, but my point of origin is farther down the line of time than many others, thus my 'proper English' is in fact not. Funny how this tends to go on through the ages. Makes me ponder the idea that there's no such thing as perfect English to begin with, since it's such a bastard/mongol language in that it incorporates everything from everyone else.

I remember growing up constantly frustrated by the use of 'an' before a word beginning with h. An horse, an house. Drove me bonkers! I was told it's 'Queen's English' and that it's the more formal proper form of the language spoken in England. In my junior year of high school, we read Pygmalion. In the back of the book were excerpts from similar books. One stood out to me: it was a father teaching his son about animals, they come across a hedgehog. He tells his boy "That's an edgeog. It's two words really: edge and og and they both start with an aitch." Then I pondered the idea that the 'Queen's English' came from the common working-class colloquial English. You would say 'an horse' and 'an house' if you didn't pronounce the h in the first place.
Ahh, my love/hate relationship with my native tongue. Plenty of other languages don't have these problems you know. ;)

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According to the OED, “perpendicular” has been used to mean “at right angles” since at least c1475 (and their earliest sighting of it used to mean “vertical” is only 25 years earlier). This usage is not new by any stretch of the imagination. The dictionary does say, however, that it is found “chiefly” in science and engineering (presumably including mathematics). Perhaps it is finding it used outside of this context that is bothering you.

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I first learned the word in sense in which it's used in the field of geometry (at right angles to a line). I learned the word "parallel" probably in the same lesson, way back in the mists of childhood memories. Perpendicular being like the opposite of parallel.

To me, that is the primary meaning, and to see the word "perpendicular" without a base reference line/plane of comparison seems odd to me. So, something being "perpendicular to" something else, or mention of "two perpendicular lines" makes sense. But if you say "a perpendicular tree", my reaction is "perpendicular to what?"

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Here are three meanings given for a right angle:

M-W: the angle bounded by two lines perpendicular to each other : an angle of 90° or 1⁄2 π radians

Webster's 1913:
(a) The angle formed by one line meeting another perpendicularly, as the angles ABD, DBC.
(b) (Spherics) A spherical angle included between the axes of two great circles whose planes are perpendicular to each other.

OED: an angle of 90°, as in a corner of a square *** or at the intersection of two perpendicular straight lines ***. (stars put in by me)
-
For me, the OED is dead wrong on that last part. Two perpendicular lines would be parallel ... for them to intersect at 90º, one must be perpendicular to the other!

@Chris, if someone says that something is "perpendicular", I'm going to assume the person means more or less straight up, vertical. A perpendicular tree would be straight up from the ground ... as opposed to a horizontal tree which is flat on the ground.

The OED, as part of the meaning for perpendicular, says:
• at an angle of 90° to the ground; vertical: the perpendicular cliff.
• (of something with a slope) so steep as to be almost vertical: guest houses seem to cling by faith to the perpendicular hillside.

I find perpendicular in "perpendicular cliff" to be unneeded ...

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@Ing
I agree with you on the everyday conversation. There are probably few occasions when one would use perpendicular.
You wouldn't say "he has a perpendicular posture", and certainly saying "the wall is at 90 degrees to the floor" is ok, although with modern building practices I guess the wall could be vertical and not be square with the floor, or even be square with the floor and not be truly vertical.
;)

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*Or you could substitute 'horizon' with 'tangent of the Earth'.

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@Hacovo
Yep, plumb would serve in some cases.
However, being a pedantic old curmudgeon, I much prefer the original pure meaning of perpendicular. But I would not attempt to force anyone on a particular usage of any word.
Interesting point on curvature of the earth: leads one to ponder the old saw about the shortest distance between two points.

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You forgot the "old".
:)
Never heard "an" being used before horse or house although I have heard it used with "hotel" by those who believe the "h" in that word to be silent.
Which then brings us to the pronunciation of herb which according to some American sources also has a silent "h".
Unfortunately what those in the south east of England term The Queen's English (or The King's English depending on who is on the throne) is a dreadul mismash of very long vowels and extra consonants.
Now I'm getting off topic, sorry.

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@njtt
From the OED online:-
A. adj.
1.
a. Situated or directed at right angles to the plane of the horizon; vertical.
a1450 (1391) Chaucer Treat. Astrolabe ii. §23. 45 Thou must have a plomet hangyng on a lyne, heygher than thin heved, on a perche; and thilke lyne must hange evene perpendiculer bytwixe the pool and thin eye.
b. Nearly vertical; very steep, precipitous.
1598 Shakespeare Henry IV, Pt. 1 ii. v. 347 That sprightly Scot of Scottes, Dowglas, that runnes a horsebacke vp a hill perpendicular.
c. Of a person: having an upright figure, bearing, or posture; erect, upright. Also: performed in a standing position; standing.
1768 L. Sterne Sentimental Journey I. 117 He canter'd away before me as happy and as perpendicular as a prince.
2. Chiefly Science and Engin. Of a line or plane: situated at right angles to a given line, plane, or surface. Usu. with to, †with.
A line is said to be perpendicular (now more usually normal) to a curve when it is at right angles to the tangent at the point of intersection.
c1475 Court of Sapience (Trin. Cambr.) (1927) 1992 Dame Geometry‥Full craftyly‥taught of euery spere‥Whyche lyne ys ryght, whyche perpendyculere [v.r. perpentyculere].

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@njtt
Certainly the out of context usage is bothersome.
However, be it prescriptivism, pedantry, or whatever, my preference is to stick to the usage which is closest to the root of the word.
In fact, outside of an engineering, scientific, or mathematical context, I had never heard it used in any other fashion until recently, and Deaver's book is the time I've seen it in print.

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@Hairy Scot

While you are right that outside of mathematics or engineering, "perpendicular" is supposed to mean "vertical", I would say that in everyday speech and print, it more common to see/hear "vertical" instead of "perpendicular" to describe something that is at right angles to the the horizon/horizontal.

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@Ing
I do not dispute that "vertical" is more commonly used than "perpendicular".
My gripe is what I see as erroneous use of "perpendicular" as typified by the example I quoted.

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FWIW Hairy Scot, I'm with yu on this one. I'v had a lot of math courses ... up thru two years of differential equations (many, many years ago) and I can't recall describing a line as perpendicular that wasn't the "up" line. A line at 0/360 deg (north) is perpendicular to the one at 90 deg (east) or 270 deg (west). but I wouldn't say that the line at 180 deg (south) is perpendicular to 90 or 270. Maybe it has changed since I had a math class, but that's the way it was xx years ago.

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@Anwulf
Thanks for your support. On a latinate derivative! :)
Loved your suggestion of "anent" as an alternative for "in regard to".
Maybe there is a case for bringing back Olde Englische.

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I like to use perpendicular as meaning "a line meeting another at a right angle, at any point on that line other than the two ends." But that's just me.

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@Hairy Scot ... LOL ... I may stay away from Latinates, but that doesn't mean that I don't kno them or how to benote them. :)

Perpendicular is a mouthful. A perpend is the vertical layer of mortar between bricks. It looks like a back-making (back-formation) from perpendicular.

I think "right angle" is better to bewrite (describe) the 90 deg angle (bend?). One could brook "bight" (OE bīht - angle) insted of angle but a bight nowadays is thought more of as a curve ... a bight in a rope is a loop.

Angle shares the same PIE root *ang-/*ank- "to bend" with ankle and angle (to fish) from OE angel (OHG ango) ... hook, OE angnere ... corner of the eye. So truly, one could eathly say the word was also in OE with a like meaning.

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Yes, widely in America herb is pronounced 'erb'. A silent h in hotel, however, I have never heard.
In any case, I don't hear much h dropping, but I had seen 'an' before h words in print in old English manuscripts, and it was the cause of much bother for me.

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@Chris
I don't know when or where you learned geometry, but when I did a line at right angles to another line was described just as that.
As I said above, a wall can be perpendicular to the floor, but the floor is at right angles to the wall and the walls of a room at right angles to each other. (Given that the builder knew his job and how to use a plumbline.)

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Please forgive the typo "is at".

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I have never heard the proper definition before and am guilty of using the word loosely. I like the idea of reserving the use of perpendicular to refer to the horizon. It gives you more of a sense of what a person is describing. It's refreshing as most words in the English language seem to lack that level of specificity.

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Merriam Webster Online gives the following:

Definition of PERPENDICULAR

1 a : standing at right angles to the plane of the horizon : exactly upright
b : being at right angles to a given line or plane

2: extremely steep : precipitous

3 often capitalized : of or relating to a medieval English Gothic style of architecture in which vertical lines predominate

4: relating to, uniting, or consisting of individuals of dissimilar type or on different levels

I guess the word that means 1a does not get used very often in everyday conversation. People mostly use "upright" or "vertical" or the phrase "standing straight up". Meaning 1b however is very commonly used in geometry and engineering terminology, where we say Line CD is perpendicular to Line AB, irrespective of the inclination of line AB to the horizontal - meaning the angle between the two lines is 90 degrees.

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@Hairy Scot
I actually said in preference to meaning 1a not 1b. I agree meaning 1a is related to pendre - pendulum, pendulous, pending

When someone says "I took a chair perpendicular to his" they probably mean that the chairs are oriented such that one is facing (say) north and the other is facing east (from meaning 1b).

I would not necessarily use "perpendicular" in everyday conversation though. I would probably say "at right angles". To describe a 90 degree orientation, sometimes the word "square" is used.
"The front wall should be square with the side wall".

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