The Notebooks of Leonardo Da Vinci

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Author: Leonardo da Vinci

777.
ON FISSURES IN NICHES.

An arch constructed on a semicircle and bearing weights on the two opposite thirds of its curve will give way at five points of the curve. To prove this let the weights be at n m which will break the arch a, b, f. I say that, by the foregoing, as the extremities c and a are equally pressed upon by the thrust n, it follows, by the 5th, that the arch will give way at the point which is furthest from the two forces acting on them and that is the middle e. The same is to be understood of the opposite curve, d g b; hence the weights n m must sink, but they cannot sink by the 7th, without coming closer together, and they cannot come together unless the extremities of the arch between them come closer, and if these draw together the crown of the arch must break; and thus the arch will give way in two places as was at first said &c.

I ask, given a weight at a what counteracts it in the direction nf and by what weight must the weight at f be counteracted.

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Chicago: Leonardo da Vinci, "777. On Fissures in Niches.," The Notebooks of Leonardo Da Vinci, trans. Richter, Jean Paul, 1847-1937 in The Notebooks of Leonardo Da Vinci (New York: Dover Publications, Inc., 1970), Original Sources, accessed September 20, 2018, http://www.originalsources.com/Document.aspx?DocID=D2NW6HLR9HU6CW7.

MLA: Vinci, Leonardo da. "777. On Fissures in Niches." The Notebooks of Leonardo Da Vinci, translted by Richter, Jean Paul, 1847-1937, in The Notebooks of Leonardo Da Vinci, New York, Dover Publications, Inc., 1970, Original Sources. 20 Sep. 2018. www.originalsources.com/Document.aspx?DocID=D2NW6HLR9HU6CW7.

Harvard: Vinci, LD, '777. On Fissures in Niches.' in The Notebooks of Leonardo Da Vinci, trans. . cited in 1970, The Notebooks of Leonardo Da Vinci, Dover Publications, Inc., New York. Original Sources, retrieved 20 September 2018, from http://www.originalsources.com/Document.aspx?DocID=D2NW6HLR9HU6CW7.