#euclideangeometry — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #euclideangeometry, aggregated by home.social.
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Proposition 4: Of all two triangles of which the angles of one are equal to the angles of the other, the sides respecting the equal angles are proportional.
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Proposition 3: If a right line drawn from any of the angles of a triangle to the base cuts that angle by equals, the two parts of that base are to be the same proportion to the remaining sides of the triangle. And if the two parts of the base, which the line drawn from the angle divides, were proportional to the remaining sides of the triangle, that line is necessarily proved to divide the angle by equals.
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Proposition 2: If a right line cutting two sides of a triangle were equidistant to the remaining, then it is to cut those two sides proportionally. And if it cuts proportionally, it is necessary for it to be equidistant to the remaining side.
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priorly: https://no-outlet.com/@ivlia/116336755502734396
Proposition 1: If there were one altitude of two rectilinear superficies of equidistant sides or of triangles, then either of them will be so much to the other as its base is to the base of the other.
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Proposition 11: If the proportions of quantities are equal to one other, then also it is necessary for the proportions themselves to be mutually equal.
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Proposition 10: If the proportion of a quantity to one other is greater, the quantity is to be the greater. But if the proportion of the one to the same is greater, then it is necessary for it to be the lesser.
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Proposition 9: If there is one proportion of some quantities to one quantity, they are to be equal. And if the proportion of the one to them is one, it is necessary they are to be equal.
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Proposition 8: If two unequal quantities are proportioned to one quantity, the greater shall indeed maintain a greater proportion, and the lesser a lesser, and of that to them, a greater proportion will be to the lesser, and a lesser to the greater.
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Proposition 7: If two equal quantities are compared to any one, the proportion of them to that will be one, and likewise the proportion of that to them is one.
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Proposition 6: If two quantities are equal multiples to two others and the two lesser are subtracted from the two greater, each from its own multiple, then the two remaining will be equal multiples of the same parts, or equal to them.
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Proposition 5: If there are two quantities of which one is part of the other and a part is diminished from each of them, the remaining will be an equal multiple to the remaining as the total is to the total.
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Proposition 4: If the proportion of the first to second will be as third is to fourth, and equal multiples are assigned to the first and to the third, and likewise equal multiples to the second and to the fourth, the multiples assigned will be proportional in the same order.
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Proposition 3: If the first to second and third to fourth are equal multiples, and equal multiples to the first and to the third are taken, the multiple of the first to the second and the multiple of the third to the fourth will be equal multiples.
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Proposition 2: If there are six quantities, of which the first to second and third to fourth are equal multiples, and the fifth to second and sixth to fourth are equal multiples, the total of the first and fifth to the second, and the total of the third and sixth to the fourth, will agree to be equal multiples.
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thence: https://no-outlet.com/@ivlia/114677842782325476
Proposition 1: If any quantities are equal multiples of the same number of any other, or each one is equal to each other, it is necessary for, as one of them is comparable to the other, the whole from these aggregated to likewise relate similarly to all those taken equally.
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Proposition 15: To describe a hexagon both equilateral and equiangular within a proposed circle. From this it is manifest that the side of a hexagon is equal to half the diameter of the circle to which it is inscribed.
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Proposition 14: To describe a circle around a given pentagon, which is equilateral and equiangular besides.
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Proposition 13: To describe a circle within an assigned equilateral and equiangular pentagon.
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Proposition 12: To designate an equilateral and equiangular pentagon around a proposed circle.
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Proposition 11: To describe an equilateral and equiangular pentagon within a given circle.
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Proposition 10: To designate a triangle of two equal sides, each of whose two angles, which the base obtains, are twice as much the remaining.
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Proposition 9: To describe a circle around an assigned quadrate.
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Proposition 8: To describe a circle within an assigned quadrate.
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Proposition 7: To describe a quadrate around a proposed circle.
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Proposition 6: To describe a quadrate within a given circle.
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Proposition 5: To describe a circle around an assigned triangle, whether it may be orthogonal, amblygonal, or oxygonal.
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Proposition 4: To describe a circle within a given triangle.
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Proposition 3: Around an assigned circle, to describe a triangle equiangular to an assigned triangle.
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Proposition 2: Within an assigned circle, to assemble a triangle equiangular to an assigned triangle.
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continuing from here: https://no-outlet.com/@ivlia/113749821408334309
Proposition 1: Within a given circle, to fit a right line equal to a given right line that is no greater than the diameter.