Posts tagged 'cube'

G.311 square number

And a:term:**cube** <cube-number> is equal:term:multiplied <G.269> by equal and again by equal, or a:term:number <G.248> which is contained by three equal numbers.

G.312 cube numbers there

Between two cube numbers there are two mean proportional numbers, and the cube has to the cube the ratio triplicate of that which the side has to the side.

G.315 cube number measure

If a cube number measure a cube number, the side will also measure the side; and, if the side measure the side, the cube will also measure the cube.

G.317 cube number measure

If a cube number do not measure a cube number, neither will the side measure the side; and, if the side do not measure the side, neither will the cube measure the cube.

G.325 numbers continued proportion

If four numbers be in continued proportion, and the first be cube, the fourth is cube.

G.327 numbers ratio cube

If two numbers have to one another the ratio which a cube number has to a cube number, and the first be cube, the second is cube.

G.329 similar solid numbers

Similar solid numbers have to one another the ratio which a cube number has to a cube number.

G.332 cube number multiplying

If a cube number by multiplying itself make some number, the product is cube.

G.333 cube number multiplying

If a cube number by multiplying a cube number make some number, the product is cube.

G.334 cube number multiplying

If a cube number by multiplying any number make a cube number, the multiplied number is cube.

G.335 number multiplying itself

If a number by multiplying itself make a cube number, it will itself also be cube.

G.337 many numbers please

If as many numbers as we please beginning from an unit be in continued proportion, the third from the unit is square, as will also those which successively leave out one; the fourth is cube, as will also all those which leave out two; and the seventh is at once cube and square, as will also those which leave out five.

G.338 many numbers please

If as many numbers as we please beginning from an unit be in continued proportion, and the number after the unit be square, all the rest is square. And, if the number after the unit be cube, all the rest is cube.

G.339 many numbers please

If as many numbers as we please beginning from an unit be in continued proportion, and the number after the unit be not square, neither will any other be square except the third from the unit and all those which leave out one. And, if the number after the unit be not cube, neither will any other be cube except the fourth from the unit and all those which leave out two.

G.548 cube

A:term:**cube** <cube> is a:term:solid figure <G.529> contained by six equal:term:squares <G.63>.

G.549 sides opposite planes

If the sides of the opposite planes of a cube be bisected, and planes be carried through the points of section, the common section of the planes and the diameter of the cube bisect one another.

G.595 construct a cube and comprehend it in a

Construct a cube and comprehend it in a sphere, like the pyramid; and to prove that the square on the diameter of the sphere is triple of the square on the side of the cube.

G.600 construct a dodecahedron and comprehend it in a

Construct a dodecahedron and comprehend it in a sphere, like the aforesaid figures, and to prove that the side of the dodecahedron is the irrational segment called apotome.

G.601 set out sides

To set out the sides of the five figures and to compare them with one another.