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#euclideangeometry — Public Fediverse posts

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  1. 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.

    #EuclideanGeometry

  2. 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.

    #EuclideanGeometry

  3. 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.

    #EuclideanGeometry

  4. 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.

    #EuclideanGeometry

  5. 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.

    #EuclideanGeometry

  6. 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.

    #EuclideanGeometry

  7. 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.

    #EuclideanGeometry

  8. 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.

    #EuclideanGeometry

  9. 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.

    #EuclideanGeometry

  10. 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.

    #EuclideanGeometry

  11. thence: no-outlet.com/@ivlia/114677842

    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.

    #EuclideanGeometry

  12. 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.

    #EuclideanGeometry

  13. Proposition 14: To describe a circle around a given pentagon, which is equilateral and equiangular besides.

    #EuclideanGeometry

  14. Proposition 13: To describe a circle within an assigned equilateral and equiangular pentagon.

    #EuclideanGeometry

  15. Proposition 12: To designate an equilateral and equiangular pentagon around a proposed circle.

    #EuclideanGeometry

  16. Proposition 11: To describe an equilateral and equiangular pentagon within a given circle.

    #EuclideanGeometry

  17. 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.

    #EuclideanGeometry

  18. Proposition 9: To describe a circle around an assigned quadrate.

    #EuclideanGeometry

  19. Proposition 8: To describe a circle within an assigned quadrate.

    #EuclideanGeometry

  20. Proposition 7: To describe a quadrate around a proposed circle.

    #EuclideanGeometry

  21. Proposition 6: To describe a quadrate within a given circle.

    #EuclideanGeometry

  22. Proposition 5: To describe a circle around an assigned triangle, whether it may be orthogonal, amblygonal, or oxygonal.

    #EuclideanGeometry

  23. Proposition 4: To describe a circle within a given triangle.

    #EuclideanGeometry

  24. Proposition 3: Around an assigned circle, to describe a triangle equiangular to an assigned triangle.

    #EuclideanGeometry

  25. Proposition 2: Within an assigned circle, to assemble a triangle equiangular to an assigned triangle.

    #EuclideanGeometry

  26. continuing from here: no-outlet.com/@ivlia/113749821

    Proposition 1: Within a given circle, to fit a right line equal to a given right line that is no greater than the diameter.

    #EuclideanGeometry

  27. Proposition 36: If a point is marked without a circle whence two lines are drawn to the circumference, one cutting and the other applied to the circumference, and that made from the whole of the secant drawn according to the extrinsic part of it is equal to that made from the applied line drawn according to itself, from necessity the applied line will be touching the circle.

    & that's book III. which was honestly pretty good. comparatively.

    IV contd: no-outlet.com/@ivlia/113964625

    #EuclideanGeometry

  28. Proposition 35: If a point is marked without a circle whence two straight lines are drawn to the circle, with one line cutting and the other touching, then that contained within the whole secant as well the extrinsic part of it, is equal to the quadrate that is drawn from the tangent line.

    #EuclideanGeometry

  29. Proposition 34: If in a circle two straight lines divide one another, that which proceeds within the two parts of one of them is equal to the rectangle that is contained within the two parts of the other line.

    #EuclideanGeometry

  30. Proposition 33: From a given circle, to abscind a portion taking an angle equal to a given angle.

    #EuclideanGeometry

  31. Proposition 8: Of all two triangles of which the two sides of one are equal to the two sides of the other: and the base of one is equal to the base of the other: it is necessary that the two angles contained by the equal sides are equal.
    #EuclideanGeometry #triangleTuesday

  32. Proposition 8: Of all two triangles of which the two sides of one are equal to the two sides of the other: and the base of one is equal to the base of the other: it is necessary that the two angles contained by the equal sides are equal.
    #EuclideanGeometry #triangleTuesday

  33. Proposition 8: Of all two triangles of which the two sides of one are equal to the two sides of the other: and the base of one is equal to the base of the other: it is necessary that the two angles contained by the equal sides are equal.
    #EuclideanGeometry #triangleTuesday

  34. Proposition 8: Of all two triangles of which the two sides of one are equal to the two sides of the other: and the base of one is equal to the base of the other: it is necessary that the two angles contained by the equal sides are equal.
    #EuclideanGeometry #triangleTuesday

  35. Proposition 8: Of all two triangles of which the two sides of one are equal to the two sides of the other: and the base of one is equal to the base of the other: it is necessary that the two angles contained by the equal sides are equal.
    #EuclideanGeometry #triangleTuesday

  36. Proposition 6:
    If two angles of a triangle are equal to the other, then the two sides respecting those angles will be equal. Quod est impossibile.
    #EuclideanGeometry #triangleTuesday