PREFACE

SYNOPSIS OF EUCLID’S BOOK OF DATA

The original text is organized into a branching tree diagram using large curly braces to classify the types of "Data," which are the known elements or given information in Euclid’s geometry. This hierarchy moves from general concepts on the left to specific examples and their corresponding proposition numbers on the right.

• By Magnitude (Size) This category deals with the physical dimensions of shapes.

  • Magnitude in general.
  • Area.
  • Straight line.
  • Angle.
  • {To which we can provide equivalents.} Propositions 2, 3, 4, 7, 52, 92, 93, 94, 95, 32, 55, 57, 58, 59, 60, 84, 85, 86, 87, 88, 33, 39.
  • Circle, whose radius original: "quæ ex centro," meaning the distance from the center is given in magnitude.
  • Segment of a circle, in which the angle and the size of the base are given.

• By Ratio, to which we can provide an equivalent. This involves the relationship between two quantities rather than their absolute size.

  • Of a straight line to a straight line 1, 5, 6, 8, 9, 22, 23, 24, 34, 53, 54, 56, 68, 69, 76, 77, 81, 94.
  • Of a rectilinear figure to a straight line.
    • Similar Figures that have the same shape but perhaps different sizes.
      • In any case: Of a triangle to a triangle 51.
    • Dissimilar
      • In a certain particular way.
        • A triangle 41, 71, 72.
        • Of a square to a triangle 63.
        • Of a rectilinear figure to a triangle 64, 65, 66, 67.
        • Of a parallelogram to a parallelogram 70, 73.

• By Species (Shape), a rectilinear figure where the angles are given and the ratios of the sides to each other are given. The term "Species" here refers to the specific form or proportion of a figure.

  • Triangles 34, 40, 41, 42, 43, 44, 45, 46, 47, 80.
  • Parallelograms
    • Any kind 61, 62.
    • Rectangles 78.

• Given by Position, which always occupy the same place.

  • Point 25, 27, 90, 96.
  • Line 28, 29, 30, 31, 35, 36, 37, 38.
  • Angle.
  • Circle whose center is given by position, and its radius is given by magnitude.

• By Position and Magnitude.

  • Segment of a circle in which the angle is given by magnitude, and the base is given by position and magnitude.
  • Straight line 26, 91.