'Euclid Elements'에 해당되는 글 13건

유클리드 원론 13권 (Euclid Elements XIII)
Propositions Proposition 1 If a straight line is cut in extreme and mean ratio, then the square on the greater segment added to the half of the whole is five times the square on the half. Proposition 2 If the square on a straight line is five times the square on a segment on it, then, when the double of the said segment is cut in extreme and mean ratio, the greater segment is the remaining part ..
Geometry/Euclidean Geometry  |  2016. 5. 10. 13:34
유클리드 원론 12권 (Euclid Elements XII)
Propositions Proposition 1Similar polygons inscribed in circles are to one another as the squares on their diameters.Proposition 2Circles are to one another as the squares on their diameters.Lemma for XII.2.Proposition 3Any pyramid with a triangular base is divided into two pyramids equal and similar to one another, similar to the whole, and having triangular bases, and into two equal prisms, an..
Geometry/Euclidean Geometry  |  2016. 5. 10. 13:28
유클리드 원론 11권 (Euclid Elements XI)
Definitions Definition 1 A solid is that which has length, breadth, and depth. Definition 2 A face of a solid is a surface. Definition 3 A straight line is at right angles to a plane when it makes right angles with all the straight lines which meet it and are in the plane. Definition 4 A plane is at right angles to a plane when the straight lines drawn in one of the planes at right angles to the..
Geometry/Euclidean Geometry  |  2016. 5. 10. 13:21
유클리드 원론 10권 (Euclid Elements X)
Definitions I Definition 1 Those magnitudes are said to be commensurable which are measured by the same measure, and those incommensurable which cannot have any common measure. Definition 2 Straight lines are commensurable in square when the squares on them are measured by the same area, and incommensurable in square when the squares on them cannot possibly have any area as a common measure. Def..
Geometry/Euclidean Geometry  |  2016. 5. 10. 13:11
유클리드 원론 9권 (Euclid Elements IX)
Propositions Proposition 1 If two similar plane numbers multiplied by one another make some number, then the product is square. Proposition 2 If two numbers multiplied by one another make a square number, then they are similar plane numbers. Proposition 3 If a cubic number multiplied by itself makes some number, then the product is a cube. Proposition 4 If a cubic number multiplied by a cubic nu..
Geometry/Euclidean Geometry  |  2016. 5. 10. 12:42
유클리드 원론 8권 (Euclid Elements VIII)
Propositions Proposition 1 If there are as many numbers as we please in continued proportion, and the extremes of them are relatively prime, then the numbers are the least of those which have the same ratio with them. Proposition 2 To find as many numbers as are prescribed in continued proportion, and the least that are in a given ratio. Corollary If three numbers in continued proportion are the..
Geometry/Euclidean Geometry  |  2016. 5. 10. 12:37
유클리드 원론 7권 (Euclid Elements VII)
Definitions Definition 1 A unit is that by virtue of which each of the things that exist is called one. Definition 2 A number is a multitude composed of units. Definition 3 A number is a part of a number, the less of the greater, when it measures the greater; Definition 4 But parts when it does not measure it. Definition 5 The greater number is a multiple of the less when it is measured by the l..
Geometry/Euclidean Geometry  |  2016. 5. 10. 12:32
유클리드 원론 6권 (Euclid Elements VI)
Definitions Definition 1 Similar rectilinear figures are such as have their angles severally equal and the sides about the equal angles proportional. Definition 2 Two figures are reciprocally related when the sides about corresponding angles are reciprocally proportional. Definition 3 A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater seg..
Geometry/Euclidean Geometry  |  2016. 5. 10. 12:25
유클리드 원론 5권 (Euclid Elements V)
Definitions Definition 1 A magnitude is a part of a magnitude, the less of the greater, when it measures the greater. Definition 2 The greater is a multiple of the less when it is measured by the less. Definition 3 A ratio is a sort of relation in respect of size between two magnitudes of the same kind. Definition 4 Magnitudes are said to have a ratio to one another which can, when multiplied, e..
Geometry/Euclidean Geometry  |  2016. 5. 10. 12:15
유클리드 원론 4권 (Euclid Elements IV)
Definitions Definition 1 A rectilinear figure is said to be inscribed in a rectilinear figure when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed. Definition 2 Similarly a figure is said to be circumscribed about a figure when the respective sides of the circumscribed figure pass through the respective angles of that about which it is c..
Geometry/Euclidean Geometry  |  2016. 5. 10. 12:05

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