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15208547 No.15208547 [Reply] [Original]

This was the entrance exam for Harvard 150 years ago. Anybody who wanted to get in had to pass this.
http://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf
Would you pass it?

>> No.15208552 [DELETED] 

>>15208547
Nigger niggers niggers niggers niggers niggers niggers niggers niggers niggers niggers Jamal Jamal Niggers NIGGERS NIGGERS NIGGERS NIGGERS NIGGERS NIGGERS NIGGERS NIGGERS NIGGERS

>> No.15208553

This was like my high school entrance exam. Easy

>> No.15208562

uh i think may be we should entertain the idea. that latin is a recent invention like mathematics, more recent than they let on temporally (yes temporal = cringe but i'll explain that), and has magical programming capabilities used to initiate people into a bad state of mind. modernity owes a lot to the proliferation of the laitn language, nno? and many of the european dreamers in the past believed they were "falling out of a box". i don't know about the more sacred shit like great-uniting-the-languages but one should continue to put it into life, not to merely ignore it because of preconceived notions. such people are lazy, the like of chodoshanden and those ernie dudes are the embodiment of the vast lazy benevolence like not being too bothered

>> No.15208653

>>15208547
Damn. Now I feel like a brainlet

>> No.15208659

I could do a bit of the section on mathematics, and that's about it.

>> No.15208662

>>15208562
Cope

>> No.15208664

>>15208547
in 5 years i hope to be able to respond the latin and greek questions. now geography and math...

>> No.15208671
File: 97 KB, 860x845, wojak-hd.png [View same] [iqdb] [saucenao] [google]
15208671

>>15208562
>>15208653
>>15208659
y'all ignant, read MOAR

>> No.15208684

>V. Leonidias, Pausanias, Lysander

Sorry what's the question?

I would have passed all the mathematics except the geometry. The geography would be hit or miss. The Latin amd Greek isn't above the level I got in high school but that was years ago and I would fail miserably now.

>> No.15208692

why greek and latin questions give in cues? is it to make it easier or harder? looks easier desu

>> No.15208711

>>15208547
This sounds pretty high school tier desu, but competent and humanities-educated highschool-tier. I would have fared better at 18 than I would now honestly.

You also have to remember the people who took the test were preprared for it.

>> No.15208717

>>15208692


The struggle with Latin is in the conjugations and genders and such, not so much in knowing the translation. So I guess they want to test mostly just that, and its also easier to score the test if everyone uses the same basic forms. You only have to check for the proper grammar.

>> No.15208729
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15208729

>>15208547
>http://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf
Guys... what's a prime number?

>> No.15208743

>>15208562
How many times was this post run through Google Translate?

>> No.15208747

>>15208729

Any number divisible (without remainder) only by itself and 1. e.g. 3, 7, or 13, but not 21 which divides by 7.
In a sense prime numbers are the only "really unique" numbers, since all non prime numbers can simply be written as a product of prime numbers. Hence you could still fully count out all the numbers if only the prime numbers existed (had their own symbol, that is).

>> No.15208757

>>15208547
i wonder if in 150 years time, we will look back at the questions in our current system are are pointless and unenlightened. maybe in just 50 years...

>> No.15208758

Maths section was suprisingly easy. Thats like high school level

>> No.15208769

>>15208659
Not geography? Those questions were pretty basic

>> No.15208771

>>15208758

Well naturally, since this exam is aimed at people coming from High School

>> No.15208777

>>15208758
retard

>> No.15208783

>>15208684
Probably their birth places

>> No.15208795

>>15208711
Yeah they would have known precisely what was going to be on it going in

>> No.15208800

>>15208758
Oh really?
>prove that circles are to each other as squares of their radii
Well, prove it (without circular logic).

>> No.15208831

>>15208547
That exam is RAYCISS!!!

>> No.15208839

>>15208729
The real question we should be asking is not what is a prime number but Who is the prime mover. If we studied more theology and less mathematics, the world would be a better place.

>> No.15208844

>>15208831
rule 6

>> No.15208869

Latin grammar seems pretty hard but I guess they were already taught it in school. The math section is brainlet tier compared to what youd be asked today.

>> No.15208879

>>15208547
If I had to take it now, I'd pass the Latin, possibly the Greek, but probably not the math and definitely not the geography. I probably wouldn't pass it. Feels bad man.

>> No.15208883

>>15208800
This question doesn't make much sense to me. The squar eof the radius appears in the value of te area of the disk. If we're talking the circle alone the radius (non squared) is enough.
>>15208795
I wonder how varied and wide-ranging was the material in those times. For instance were they certain to get questions about Athenian political figures? If yes, how many public figures did they have to know about in order to have their bases covered?

>> No.15208902

>>15208883
>The squar eof the radius appears in the value of te area of the disk. If we're talking the circle alone the radius (non squared) is enough.
Prove it.

>> No.15208924

>>15208839
Yet Aquinas should have studied maths because he didnt understand infinite sets

>> No.15208926

>describe the route of the Ten Thousand
Do this RIGHT NOW /lit/ this is referring to Xenophon and co right?

>> No.15208927

>>15208800
Not that guy but,
Area of a circle A = pi*r^2. Let Circle b be t times as large as Circle c, so A_b = t*A_c, then clearly pi*(r_b)^2 = t*pi*(r_c)^2 which is equivalent to (r_b)^2 = t*(r_c)^2. So a circle that is t times as large has t times the square of the radius.

Trivial really.

>> No.15208937
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15208937

>>15208927
>Area of a circle A = pi*r^2.
This is circular reasoning: you're assuming the result. The question asks you to prove that there's some constant c such that [math]A=cr^2[/math]. This c happens to be [math]\pi [/math] but that's beside the point.

>> No.15208969

>>15208937

It most certainly isn't. The prelude to that question asked me to show how I can find the area of a circle. Having done so I am absolutely allowed to use the fact that the area of a circle is pi*r^2 in the following question.

>> No.15208974

>>15208937
nice
>>15208969
cope

>> No.15209001

>>15208937
>The question asks you to prove that there's some constant c such that [math]A=cr^2[/math].

It doesn't.

>>15208974

t. never took a math exam in his life

>> No.15209014

>>15208902
The point is that the question is vague. It surely made sense in the terminology of the time, but there are plenty of way two shapes can "be to be each other like something".

But in any case the simplest way to approach the problem is to notice that two concentric circles (circles that share the same center) are image of one another by an homothety centered on their common center. it simply follows from the definition : if C1 is the set of points at distance exactly d from a given point A and C2 the set of points at distance exactly d' > d from A, then the application :

M -> d'*(M - A)/d

sends every point M of C1 into a point of C2 (and conversely with the application M -> d'(M-A)/d). Then with p1 the permiter of C1 and p2 the perimeter of C1, the relations :

p1 = d/d' p2 and p2 = d'/d p1

hold. Since d (respectively d') are the distance of the points of C1 (respectively C2) to the center, they are the respective radii of the circles.

The same argument gives use the relations :

a1 = (d/d')^2a2 and a1 = (d'/d)^2a1

where a1 and a2 are the respective areas of the circles.

But as always the issue is what is assumed to be true and what is assumed to be known. In modern terms you would need an integration to compute the perimeters and areas. At the time maybe it was considered self-evident, or maybe you had to use comparison with polygons or something else.

>> No.15209042

>>15208547
Actually could have fucked on the math portion. Not the latin though because it's a dead language and learning it is for doctors(medical) and psueds.

>> No.15209056

>>15209001
>It doesn't.
That's literally an equivalent formulation of the question.
> Show that x is proportional to y as z^2 is to w^2 where x and y are functions of z and w, respectively
This is equivalent to showing that x/y = z^2 /w^2 which is in turn equivalent to showing that x=cz^2 for all pairs x,z.

>> No.15209062

>>15208879
The math is very easy to learn. Maybe half a year of classes even if you have really shoddy math knowledge.

>> No.15209079

>>15209014
Are you aware that not all 2d shapes scale with the square of their length? For example, fractals have fractional scaling constants. For them, A=ar^1.5 for example, instead of r^2. Essentially, this question asks you to prove that the circle is not a fractal that its area scales nicely with its length.

>> No.15209095

>>15209056
>x is proportional to y as z^2 is to w^2 where x and y are functions of z and w, respectively

But that is false, or rather not necessarily true. Hence how could it possibly be an equivalent formulation of something that is true?

>> No.15209101

>>15209095
This is false in general, but true for the circle which is what the question is asking about.

>> No.15209115

>>15209042
Cope.

>> No.15209125

>>15208547
i wouldn't have passed the part on geography. it's frustrating.

>> No.15209131
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15209131

So, is no one seriously able to solve the question?
>tfw 1899 retards are smarter than /lit/

>> No.15209133

>>15209079
Yes, that why I said ultimately you have to use an integral if you really want to prove it, but I doubt that's what was expected on this Harvard exam.

And even when you look at it, the notion of integral is defined so that, in particular, it recovers the usual values for the areas of polygons and circles. Any theory of integration that would not have given pi*r^2 as an area for the circle would have been instantly abandoned (or heavily modified) by even its creator.

Which showcases the circular nature of the problem : at the end of the day you want the area to be of the form C*r^2 because it conforms to intuition. Theories cement, prove and further intuitions and sometimes run counter to it, but they must still agree with the most basic intuitions they apply to.

>> No.15209149

>>15209131
Honestly the guy who wrote the exam probably expected one of the answer already given itt, it's only /lit/ is autistic enough to question the validity of a highschool level proof (which is a good thing).

>> No.15209159
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15209159

>>15209133
>Yes, that why I said ultimately you have to use an integral if you really want to prove it, but I doubt that's what was expected on this Harvard exam.
No you don't, there's an elementary alternative. A bright high school student without any knowledge of integrals would definitely be able to prove it.
>And even when you look at it, the notion of integral is defined so that, in particular, it recovers the usual values for the areas of polygons and circles. Any theory of integration that would not have given pi*r^2 as an area for the circle would have been instantly abandoned (or heavily modified) by even its creator.
True, but the fact that something is intuitively true does not constitute a proof of it.
> Which showcases the circular nature of the problem : at the end of the day you want the area to be of the form C*r^2 because it conforms to intuition.
The problem is not circular. I am able to prove that it's of the form C*r^2 as opposed to some other 2d shapes. Are you?

>> No.15209168

>>15209131

Its been answered for you several times. You're just so butthurt about the fact that you got btfo that choose to dispute them on false grounds.

>> No.15209186

>>15209159
>>15209131

kys retarded anime poster

>> No.15209189

>>15208547
I could have done the math section although I have to do a bit of a refresher on that now tbqh.

>> No.15209211
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15209211

>>15209168
It hasn't. All proofs so far have been
1. circular
2. wrong
If the problem asks you to prove some statement, you can't just assume the obviously stronger form of the statement and call it a proof.
>>15209186
seething mathlet

>> No.15209212

>>15208758
>thats like high school level
Fascinating, isn't it? I wonder why.

>> No.15209225

>>15208547
Nice. We should make this the /lit/ entrance exam.

>> No.15209230
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15209230

>>15208758
>>15209212
To be fair, the last question that I posted here is a little bit higher level than the average high school question. A bright high schooler could figure it out, sure but the fact that no one on /lit/ can tells a lot.

>> No.15209233

>>15209211

When a problem asks me to prove something I can absolutely use a statement I've been asked to show in an earlier question. Fucking mouthbreather.

>> No.15209304
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15209304

>>15209233
Ok then, how did you answer the previous question?

>> No.15209323

>>15209131
are you?

>> No.15209369

>>15209323
Of course!

>> No.15209374

>>15209304

Using the fact that the circumscribing n-sided polygon has area of half it's circumference times the distance to the center of the circle, we see that as n tends to infinity, the distance to the center tends to the radius of the circle r, and the circumference tends to the circumference of the circle 2*pi*r. Hence we conclude that the circle has area 1/2*2*pi*r*r = pi*r^2.

I'm sure you now want me to proof the circumference of the circle, which I will not do because you will then have me prove everything down to 1+1=2.
stupid anime nigger.

>> No.15209390

>>15209369
prove it

>> No.15209393
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15209393

>>15209374
I guess that's as good as I am going to get from /lit/...

>> No.15209443
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15209443

>>15209390
Bound the area of the excess above with rectangles of width 2rsin(t) and height r(1-cos(t)) where t is the angle of one of the triangles (i.e. 360/n degrees). We have n such triangles so the total excess is 2 n r^2 sin(t)(1-cos(t)) = 2r^2 * 360 sin(t)(1-cos(t))/t.
Now you can prove that sin(t)/t tends to a constant because (in radians) sin(t)<t for t small enough, and (1-cos(t)) tends to 0 so the total excess area tends to 0 and so the are of the regular polygon does indeed tend to the area.
Simple.

>> No.15209471

>>15208747
>In a sense prime numbers are the only "really unique" numbers, since all non prime numbers can simply be written as a product of prime numbers.

Lmao, this is a pretty hilarious take. By that logic why not just go all the way and say that every number can be written as a sum of 1s, making 1 the only "really unique" number?

>> No.15209499

>>15208926
Yes. I think they landed in Syria somewhere and the battle took place near the Euphrates, then they crossed and followed the Tigris to Niveneh, then went North into Armenia and then hit the Black Sea? Been a while since I read it

>> No.15209535

>>15208547
this is like elementary school tier wtf?

>> No.15209537

>>15209471

>say that every number can be written as a sum of 1s,

Because how would you count those numbers? How would you describe 7 as a sum of ones? Surely not by saying you must sum 1 seven times.

We could perform all the math there is without ever needed a symbol for the number 4. We could simply replace all instance of 4 by the term 2*2. However with primes this is not possible. We need some symbol for 7, or else we could not express it.

>> No.15209567

>>15208562
seems like you are pretty confused, and are talking about stuff you have no idea of.
I'm not talking about your english as many of us are not native speakers, but for the "forma mentis" that transpires by your way of explaining your logic.

>> No.15209587

>>15208547
seems pretty easy to me, despite not opening any school book for more than 20 years I know most of the answers, I would have easily passed it back in the day, but I studied latin in highschool, so obviously not everyone could pass it.

>> No.15209618

>>15209567
You're probably right. I'm not low IQ but pretty ignorant. Anyway Nick Land has spoken about the strange effects of switching from a letter-based number system to a fully arabic one—that much of numerology stems from the fact that numbers used to literally spell things out, and possess associations with deities and supernatural forces (IV = IVPITER = Jupiter). Latin numerals make that fun for human beings, a window into our origins. (Which is why Christian numerology still works.) Yet when people talk about numerology, they really mean color numerals. Notice how just saying "two" looks almost meaningless to many people—as if it has no meaning or significance whatsoever.

>> No.15209669

>>15209537
1+1+1+1+1+1+1 = the quantity previously known as 7
???

>> No.15209879

>>15209669

You effectively described seven now though. You are right in a sense of course that 1 is the only real number, because everything just is a repeated addition of ones. Doesn't change the fact that you could express all possible numbers using only primes and this makes them more important than the set of non-primes.

>> No.15209895

>>15209211
>>15209393
is it that its dim = 2 and thus scales on a n^2 factor by definition of dimension? im not even certain of that formulation of dim even existed back then, also how would you prove that a square and a circle is of dim 2in the first place asides from "well obviously"?

>> No.15209922

>>15209159
>No you don't, there's an elementary alternative.
The question is what does the "elementary" alternative assumes.

>True, but the fact that something is intuitively true does not constitute a proof of it.
Might point is that the relationship is not only from intuitions to proof that sanction the validity of the intuition. The ability to confirm basic intuitions is a criteria for choosing a system of proof. The relationship goes both way, is what I'm saying.

>The problem is not circular. I am able to prove that it's of the form C*r^2 as opposed to some other 2d shapes.
Again, the question is, assuming what, and using what? Fractal were unknown at the time the exam in the OP was written, so the intended meaning of the question is certainly not "prove that a diskes hausdorff dimension is exactly 2".

>> No.15209935

>>15208547
It's hard to tell if I could've passed if I were educated as such. As of now, Algebra I could've without thinking, Latin I would've gotten 1/3 maybe, Greek 0, and Geography very close to zero. I do, however, think we've moved to being operators of machines rather than knowing or having something inside of us

>> No.15209948

>>15208547
And to imagine John F. Kennedy got in with mediocre grades by writing a short letter about how his father was a "Harvard man" and how he'd very much like to be a Harvard man as well.

>> No.15209953

>everyone saying that the math section is easy
Are you people baiting or am I that much of a brainlet?

>> No.15209960

>>15208547
damn oldfags had it easy

>> No.15209965

>>15209471
Both work actually, only prime numbers are the multiplicative atoms (if you will) of the integer, will 1 is the only additive atom. Both description make sense algebraically.

>> No.15209977

>>15209953
With the exception of a few tedious calculations (finding cube roots by hand) it’s all stuff you should have learned in middle school

>> No.15209978

>>15209953
The calculations is hard, algebra is easy. My guess is I'd have been able to do the rest if I were educated for it.

>> No.15210011

>>15209977
You might use the first few terms of taylor expansions to fin the root cubes.

>> No.15210037

>>15209042
Also for classical singers

>> No.15210072

>>15208684
>>15208783
It's clearly Sparta

>> No.15210095

>>15208547

>Describe the route of the Ten Thousand

I'm sorry did you mean, the six gorillion?

>> No.15210484

>>15209230
t. 60iq retarded anime incel

>> No.15210506

>>15209953
The only section I knew anything about was geography. The languages and math were all difficult to me.

>> No.15210564

>>15208547
Naw i'd fail it, but really interesting study material.

>> No.15210596

>>15208547
I would simply write black lives matter over the whole thing

>> No.15210600

>>15210506
The language section isn't a problem; one can study latin and greek and learn it satisfyingly enough if he wants to. The same goes with geography and history. What I found the most concerning is my utter lack of knowledge of math. I did study it in high school, but not too much. I recall being able to get algebra more easily than the other branches, but that's about it.

>> No.15210752

>>15208547
"Bound the basin of the Po"

Do they give you a map of Italy or do I have to draw the whole damn thing?

>> No.15210782

>>15210600

Math major here, other way round for me.

Also I can name every current country, its capital, identify its flag, know hundreds of regions of larger/relevant countries, lots of other geography data. But my weak spot is rivers (something I've been meaning to improve on but haven't) so naturally the exam focuses on these.

>> No.15210788

why such a large emphasis on the ancients?

>> No.15210830

brainlet here, would that suffice as the proof of the fact that circles are to each other as the squares of their radii?
>all circles are similar
>therefore their circumferences are to each other in the same ratio as their radii
>therefore their areas are to each other as ratio of squares of their radii

>> No.15210917

>>15210788
Must have filter the plebs somehow.

>> No.15210918

>>15210782
>other way round for me
Why do you think this? You can easily open wikipedia articles and read about history, geography etc.
It takes more intelligence to grasp math, physics and the natural sciences in general.

>> No.15211367

>>15210918

True but to understand historical events and the relevance of geography you have to have some grasp on how people act and why, which mathlets don't.

>> No.15211427

>>15208547
nope, not in the slightest, I would need preparation for the math part, since I like math theoretically but can't be arsed to solve equation/remember the right rules at the right time

>> No.15211447

>>15208800
just use square logic

>> No.15211549

>>15208547
>http://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf
nope, not even close lol

>> No.15211656

>>15209471
But we do that... One of the ways we construct the Natural Numbers is by basically adding 1 to itself over and over. (See the peano axioms and the successor function.)

You also do this a lot in algebra, i.e. considering an element of a group as a sum of the identity.

>> No.15211707

>>15208671
reading classics won't make me solve math problems very well, you nerd

>> No.15211868
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15211868

>>15208547
>greek and latin
zero knowledge
>geography
bretty good other than the 10,000 and some of the other Greek people. I was in trivia club in high school.
>math
I know the correct method for almost every question, I would need to look over my old notebooks but assuming I was fresh out of high school, I would have done well.

>> No.15212033

If you can't pass it you shouldn't be able to post on /lit/. That's how we make the board good.

>> No.15212730

>>15212033
You couldn't've passed it yourself.

>> No.15212757
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15212757

>>15211707
Yes, it will.

>> No.15212956

>>15208562
You are onto something here for sure. Hardcoding of subject/object distinctions.

>> No.15212991

I'd just spam I WANT TO GO TO HARVARD and bypass this entirely.

>> No.15213005

>>15208664
In 5 years I hope to do functionally respond to the language questions as well, but we'll see about math.

>> No.15213025

>>15208547
Books for buffing up on geography knowledge?

>> No.15213038

>>15209953
>it's ok anon, maybe u forgot about it

>> No.15213039

>>15208758
You aren't very bright are you

>> No.15213055

>>15209953
If you haven't had a math class in a decade I can understand

>> No.15213067

Is the second river from the Alps question the Danube even though they mention it in the next question?

>> No.15213085

And what does compare Athens with Sparta mean?

>> No.15213088

>>15209953
I graduated HS 10 in 2010 and forgotten most of this shit, although i do recall i once had to do it. Im more ashamed at how rusty my Latin has become

>> No.15213098

>>15213088
Graduated HS same year, is this board mostly people 23-35?

>> No.15213113

>>15213098
Dunno, but this decade feels like it flew by, especially 2015-2020

>> No.15213114

>>15213098
There are people of all ages here. Mostly just 18-20 year olds though

>> No.15213137
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15213137

>hurr durr if you don't know these answers off the bat you're a brainlet

With proper preparation and study this exam is doable. Also this exam tests useless knowledge; I can solve all the math problems in like 10 minutes with my TI-89 and nobody gives a fuck about Latin, Greek, and obscure geography.

>> No.15213148

>>15213137
Kill yourself plebeian.

>> No.15213182

>>15213137
Everyone is just saying the math is easy enough. not the other questions

>> No.15213223

>>15213137
Knowing Latin and Greek was more important back then because they would read original sources written in those languages

>> No.15213512

>>15213137
>most widely known rivers in the world
>obscure geography

>> No.15213533

>>15213512
rivers are a eurocentric social construct

>> No.15213585

>>15213148
no u
>>15213182
The math is easy in the sense that the processes are easy to learn. The test has the hardest examples possible and honestly I probably couldn't do it off the top of my head right now, but if I reviewed my stuff or just used a calculator or something like MATLAB i'll give you an answer in 10 seconds

>>15213223
I see your point but again those students would have already gone through extensive schooling to be able to translate English into Latin. I imagine it can't be hard if you've had the practice

>>15213512
Sorry I don't know the source for the Danube off the top my head, guess I'm clinically retarded now

>> No.15213586

>>15209393
Source?

>> No.15213617

>>15213512
Have you ever taken a modern geography exam (like, say, Geography HL)?
The data tested is certainly not up to modern standards.

>> No.15213682
File: 1.04 MB, 1200x901, 80910717_p0_master1200.jpg [View same] [iqdb] [saucenao] [google]
15213682

Anime anon here that challenged others on the ratio of squares question. Turns out I was completely wrong and the problem is indeed quite trivial. Once you have a covering of simple shapes of the circle you can scale them and since each simple shape scales like the square of the length, the area as a whole scales as the square of the radius.
The statement I made about how not all 2d shapes have this property is also wrong. I was thinking of fractals and how they can have fractional dimension but it's not the same as their volume, essentially I was mixing two things. You can look into how fractal dimension is calculated, it's very interesting.
I apologize to the anons I confused and hope this brings some clarity to the topic.
Have a good day.

>> No.15214483

>>15208547
I could do the Latin section with effort

>> No.15214492

>>15208547
It's all things I should know but didn't learn because I went to a rural American high school and even modern American colleges are jokes.

>> No.15216018

I could do the maths, except for the geometry. Might be able to do the geometry, didn't try. Might be able to conjugate a couple of things in greek and get a few geography questions. The rest would be a hard fail.

>>15208684
Probably wants you to briefly describe them (birthplaces, major deeds, whatever).

>> No.15216022

>>15212730
Well in fairness, I shouldn't be posting on /lit/.

>> No.15216047

>>15208547
No. Because I don't speak Latin.

Latin was the language of scholars. You could pretty much tell if someone was educated or not simply by their Latin ability. Most commoners didn't know it.

Now, how many Americans would be able to pass this test if it were in English?

>> No.15216050

Could do the maths but the rest honestly no idea