Strength of a beam and the balance of suspended rods
A prism resists far more lying flat than upright; how a rod hung between two cords shares its weight
The upper notes state a rule of the strength of materials: a uniform prismatic support ten thicknesses long that resists 1000 upright will resist 100,000 laid flat, sketched as two beams lying down and one standing with the numbers 100000, 10000, 1000. The larger lower study treats a rod suspended from two cords, showing with a column of fractions how the weight is apportioned to each cord and how the portion projecting beyond the cords relates to the portion enclosed between them. A short note fixes the centre of weight of each balance arm at the centre of its length. Marginal remarks add that the remainder is quadruple, or triple, of the whole.
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A prism resists a hundred times more lying flat than standing upright
A support of uniform thickness, angles and sides, ten thicknesses long, resists 1000 standing upright and 100,000 laid flat. Since the tenth part of its height resists 10,000 when upright, ten such square supports lying along its length come to bear 100,000 of the first weights.
Centre of weight of a balance arm
The centre of the weight of each arm of the balance lies at the centre of its length. The note accompanies small figures of suspended rods.
A rod hung by two cords shares its weight
A rod suspended by its ends from two cords of equal height distributes its weight equally to those cords. If one cord is moved toward the middle, the part enclosed between the cords is no longer shared equally, and the weight transferred to the moving cord is proportional to the motion made by that cord along the rod.
Fractions of the rod's overhang
The column of figures works out that the length of rod projecting beyond the two cords is one ninth of the length enclosed between them, and continues through eighths, sevenths, sixths, fifths, quarters and thirds. The letters a, b, c label the reckoning.