Posts tagged 'gnomon'
G.86 gnomon
And in any parallelogrammic area let any one whatever of the parallelograms about its:term:diameter <G.61> with the two complements be called a:term:**gnomon** <gnomon>.
G.87 rectangle on unequal parts plus square on difference
If a segment is cut into equal and unequal parts, the rectangle contained by the unequal parts together with the square on the segment between the points of section equals the square on the half.
G.88 rectangle on bisected and extended segment
If a segment is bisected and a segment is added to it in a line, the rectangle contained by the whole with the added segment and the added segment together with the square on the half equals the square on the segment made up of the half and the added segment.
G.89 square of a difference
If a segment is cut at random, the sum of the squares on the whole and on one of the parts equals twice the rectangle contained by the whole and that part together with the square on the remaining part.
G.90 four rectangles plus square on difference
If a segment is cut at random, four times the rectangle contained by the whole and one of the parts together with the square on the remaining part equals the square on the whole and the first part as one segment.
G.239 parallelograms applied segment
Of all the parallelograms applied to the same segment and deficient by parallelogrammic figures similar and similarly situated to that described on the half of the segment, that parallelogram is greatest which is applied to the half of the segment and is similar to the defect.
G.240 segment apply parallelogram
To a given segment to apply a parallelogram equal to a given polygon and deficient by a parallelogrammic figure similar to a given one: thus the given polygon must not be greater than the parallelogram described on the half of the segment and similar to the defect.
G.241 segment apply parallelogram
To a given segment to apply a parallelogram equal to a given polygon and exceeding by a parallelogrammic figure similar to a given one.
G.477 area contained rational
If an area be contained by a rational segment and a first apotome, the “side” of the area is an apotome.
G.478 area contained rational
If an area be contained by a rational segment and a second apotome, the “side” of the area is a first apotome of a medial segment.
G.479 area contained rational
If an area be contained by a rational segment and a third apotome, the “side” of the area is a second apotome of a medial segment.
G.480 area contained rational
If an area be contained by a rational segment and a fourth apotome, the “side” of the area is minor.
G.579 segment cut extreme
If a segment be cut in extreme and mean ratio, the square on the greater segment added to the half of the whole is five times the square on the half.
G.580 square segment five
If the square on a segment be five times the square on a segment of it, then, when the double of the said segment is cut in extreme and mean ratio, the greater segment is the remaining part of the original segment.
G.581 segment cut extreme
If a segment be cut in extreme and mean ratio, the square on the lesser segment added to the half of the greater segment is five times the square on the half of the greater segment.
G.582 segment cut extreme
If a segment be cut in extreme and mean ratio, the square on the whole and the square on the lesser segment together are triple of the square on the greater segment.