Euclid's Elements

Given two unequal straight lines, to find that by which the greater has more power than the smaller. 132
Given two straight lines, how to find that which measures them.
If a whole magnitude composed of two magnitudes is incommensurable to one of the components, the remainder will also be incommensurable. 133
If a parallelogram is applied to a certain straight line, deficient by a square figure, the applied parallelogram is equal to the rectangle which is contained by the parts of the straight line made by the application. 133.b.
If two straight lines are unequal, and the fourth part of the square which is made from the smaller is applied to the larger, deficient by a square figure, the applied part does not pass through the bipartition section.
Given two unequal straight lines, to apply the fourth part of the square of the smaller to the larger, so that it is deficient by a square figure.
To cut a given straight line so that the rectangle which is contained by the parts is equal to a given rectilinear figure. However, it is necessary that the given rectilinear figure be smaller than the square which is described from the half. 134.b.
To divide a given number into two parts so that the product made from them is equal to a given number; however, it is necessary that the given number, to which it must be equal, be smaller than the square of the half.
Rational magnitudes are commensurable. 135.b.
To find two rational magnitudes commensurable in power.
A magnitude commensurable to a rational one is itself rational. 136
The rectangle contained by two given rational straight lines will be a given meaning "defined" or "known" area. 136.2.
If a given area is applied to a given rational straight line, the width it makes will be given. 136.b.
A straight line which is composed of two rational straight lines commensurable in length will be given. 137.b.
The difference of two given rational lines, which are unequal and commensurable in length, will be given. 138
To find two rational lines commensurable only in power. 138.b.
A straight line which has the power to form an irrational area is irrational. 138.b.
A medial is an irrational which has the power to form an area contained by rational lines commensurable only in power. 139.2.
A medial, which is one of the irrationals, is to be considered in geometric analogy.
If there are two straight lines, it will be as the first is to the second, so the square made from the first is to the rectangle contained by the two straight lines. 136.b.2.
An area commensurable to a medial area is medial. 140.b.
The rectangle contained by two given medials, or a medial and a rational, will be given. 141.2.
If a given area is applied to a given medial, the width it makes will be given.
A straight line composed of two given medials commensurable in length will be given. 141.b
The difference of two given medials, which are unequal and commensurable in length, will be given. 142.2.
A rational does not exceed a rational except by a rational. 143.b.
To find two square numbers such that the one composed of them is also a square. 144.b.
To find two square numbers such that their excess is a square. 144.b.
To find two square numbers such that their excess is not a square.
If there are two straight lines in some ratio, it will be as a straight line is to a straight line, so the rectangle contained by the two straight lines is to the square of the smaller. 146
If there are three straight lines in some ratio, it will be as the first is to the third, so the rectangle contained by the first and the mean is to that which is contained by the mean and the third. 146.b.
From two irrational areas composed together, a whole is made rational. 148
A given straight line, which is made from two or more names referring to binomial or polynomial irrationals, and its square will be given. 148.b.
Given two straight lines which consist of two or more names, and the rectangle contained by them will be given. 149
The square of a given apotome will be given.
Given two straight lines of those which we call apotomes, and the rectangle which is contained by them will be given.
A given straight line, which is made from two or more names, and a given apotome, the rectangle which...