Posts tagged 'similar-plane-and-solid-numbers'
G.318 similar plane and solid numbers
Similar plane and solid numbers are those which have their sides:term:proportional <G.180>.
G.319 similar plane numbers
Between two similar plane numbers there is one mean proportional number; and the plane number has to the plane number the ratio duplicate of that which the corresponding side has to the corresponding side.
G.321 similar solid numbers
Between two similar solid numbers there fall two mean proportional numbers; and the solid number has to the similar solid number the ratio triplicate of that which the corresponding side has to the corresponding side.
G.322 mean proportional number
If one mean proportional number fall between two numbers, the numbers is similar plane numbers.
G.323 mean proportional numbers
If two mean proportional numbers fall between two numbers, the numbers are similar solid numbers.
G.324 numbers continued proportion
If three numbers be in continued proportion, and the first be square, the third is square.
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.328 similar plane numbers
Similar plane numbers have to one another the ratio which a square number has to a square number.
G.329 similar solid numbers
Similar solid numbers have to one another the ratio which a cube number has to a cube number.
G.330 similar plane numbers
If two similar plane numbers by multiplying one another make some number, the product is square.
G.331 numbers multiplying make
If two numbers by multiplying one another make a square number, they are similar plane numbers.
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.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.381 squares segments commensurable
The squares on segments commensurable in length have to one another the ratio which a square number has to a square number; and squares which have to one another the ratio which a square number has to a square number will also have their sides commensurable in length. But the squares on segments incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides commensurable in length either.
G.383 find two segments incommensurable
Find two segments incommensurable, the one in length only, and the other in square also, with an assigned segment.