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Land surveying, the art of measuring horizontal and vertical distances between objects, demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

Land surveying - is singular. Thus, the correct verb is "demands".
"ability To " is correct construction.
We can eliminate choices A, B and C easily.

E says - Land surveying demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart...
implies " particularly command of ability to ..." - that's nonsensical. Having a command of something itself is the ability.

D survives without any issue.
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1)Land Surveying, the main subject, requires Singular verb i.e demands i.e A and B out
2)Ability of/for is unidiomatic; "Ability to" is correct C is out
3)In E Particularly of the ability is wrong also Which wrongly modifies Celestial bodies +verb is singular for "Which" -Eliminate E

D is the answer
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Land surveying, the art of measuring horizontal and vertical distances between objects, demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

First, "Land surveying" is singular --> demands --> A & B out

(A) demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

(B) demand a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart, in relation to the curvature of the rotating Earth, the course of celestial bodies.

(C) demands a strong command of trigonometry and astronomy, with the ability for mathematically charting the course of celestial bodies in relation to the curvature of the Earth that is rotating. --> with the ability, which modifies land surveying, incorrect

(D) demands a strong command of trigonometry and astronomy, particularly the ability to mathematically chart the course of celestial bodies in relation to the curvature of the rotating Earth. --> demands the ability to...; correct

meaning: the ability to chart "the course of celestial bodies in relation to the curvature of the rotating Earth"

(E) demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart the course of celestial bodies, which is related to the curvature of the Earth that rotates. --> demands of the ability to....; incorrect

meaning: the ability to chart the course of celestial bodies; which distorts the meaning of the original sentence
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generis

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Land surveying, the art of measuring horizontal and vertical distances between objects, demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

(A) demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

(B) demand a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart, in relation to the curvature of the rotating Earth, the course of celestial bodies.

(C) demands a strong command of trigonometry and astronomy, with the ability for mathematically charting the course of celestial bodies in relation to the curvature of the Earth that is rotating.

(D) demands a strong command of trigonometry and astronomy, particularly the ability to mathematically chart the course of celestial bodies in relation to the curvature of the rotating Earth.

(E) demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart the course of celestial bodies, which is related to the curvature of the Earth that rotates.

IMO D

Land surveying should follow a singular verb hence demand is wrong - A and B out

(C) demands a strong command of trigonometry and astronomy, with the ability for mathematically charting the course of celestial bodies in relation to the curvature of the Earth that is rotating. --> with the ability for mathematically is wrong, hence C out

(D) demands a strong command of trigonometry and astronomy, particularly the ability to mathematically chart the course of celestial bodies in relation to the curvature of the rotating Earth.

(E) demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart the course of celestial bodies, which is related to the curvature of the Earth that rotates. --> which refers to the celestial bodies . That's wrong hence E out
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Land surveying, the art of measuring horizontal and vertical distances between objects, demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

(A) demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth. Incorrect

(B) demand a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart, in relation to the curvature of the rotating Earth, the course of celestial bodies. Incorrect

(C) demands a strong command of trigonometry and astronomy, with the ability for mathematically charting the course of celestial bodies in relation to the curvature of the Earth that is rotating. Incorrect

(D) demands a strong command of trigonometry and astronomy, particularly the ability to mathematically chart the course of celestial bodies in relation to the curvature of the rotating Earth. Correct

(E) demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart the course of celestial bodies, which is related to the curvature of the Earth that rotates. Incorrect

POE -

Land surveying singular, so demand should be demands ; Eliminate A & B
ability to correct idioms, and C has redundant problem; Eliminate C
E has redundant problem and which modifier changes intended meaning

Answer D
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Land surveying, the art of measuring horizontal and vertical distances between objects, demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.

(A) demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth. -> "Land surveying" needs singular noun, so, "depend" is incorrect.

(B) demand a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart, in relation to the curvature of the rotating Earth, the course of celestial bodies. -> same as A. Incorrect.

(C) demands a strong command of trigonometry and astronomy, with the ability for mathematically charting the course of celestial bodies in relation to the curvature of the Earth that is rotating. -> "with the ability for" is incorrect.

(D) demands a strong command of trigonometry and astronomy, particularly the ability to mathematically chart the course of celestial bodies in relation to the curvature of the rotating Earth. -> There is no such error and meaning wise it makes sense too. Let's keep it.

(E) demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart the course of celestial bodies, which is related to the curvature of the Earth that rotates. -> which modifies "celestial bodies", meaning changed. Incorrect.

So, I think D. :)
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Land surveying
--------, the art of measuring horizontal and vertical distances between objects,
demand a strong command of trigonometry and astronomy,
and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth.


Error Analysis:
1. Sentence has Subject Verb (SV) Error- Land Surveying - Demand
2. here "and" has been used parallel marker - but second part is not making sense. Land surveying the ability of mathematically ???

POE

(A) demand a strong command of trigonometry and astronomy, and the ability of mathematically charting the course of celestial bodies in relation to the curvature of the rotating Earth. - SV Error and structural error

(B) demand a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart, in relation to the curvature of the rotating Earth, the course of celestial bodies. - SV Error and structural error

(C) demands a strong command of trigonometry and astronomy, with the ability for mathematically charting the course of celestial bodies in relation to the curvature of the Earth that is rotating. - Idiom Error and also appears to have modification error (with the ability ....)

(D) demands a strong command of trigonometry and astronomy, particularly the ability to mathematically chart the course of celestial bodies in relation to the curvature of the rotating Earth. - clear and concise in meaning - CORRECT

(E) demands a strong command of trigonometry and astronomy, particularly of the ability to mathematically chart the course of celestial bodies, which is related to the curvature of the Earth that rotates. - sentence appears to have 2 modification error
- demands - particularly of the ability
- celestial bodies is related to the curvature of the Earth that rotates
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