
this implies the use of similar triangles in the way that the Egyptians had used them in the construction of pyramids
Achimedes (1920)
The First Part, Chapter 11, p. 80-81
Leviathan (1651)
this implies the use of similar triangles in the way that the Egyptians had used them in the construction of pyramids
Achimedes (1920)
"On The Natural Inequality of Men" (January 1890)
1890s
Journal of Discourses 12:262 (Aug. 9, 1868)
1860s
Proposition XV. Thereom VIII.
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)
“If two right lines cut one another, they will form the angles at the vertex equal.”
...
This... is what the the present theorem evinces, that when two right lines mutually cut each other, the vertical angles are equal. And it was first invented according to Eudemus by Thales...
Proposition XV. Thereom VIII.
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)
Source: The Cruise of the 'Nona (1925), pp. 48-9
Belloc writes that Cardinal Manning said this sentence to him "when I was but twenty years old" (p. 47), i.e. in 1890 or 1891.
Context: The profound thing which Cardinal Manning said to me was this: all human conflict is ultimately theological. […]This saying of his (which I carried away with me somewhat bewildered) that all human conflict was ultimately theological: that is, that all wars and revolutions, and all decisive struggles between parties of men arise from a difference in moral and transcendental doctrine, was utterly novel to me. To a young man the saying was without meaning: I would almost have said nonsensical, save that I could not attach the idea of folly to Manning. But as I grew older it became a searchlight: with the observation of the world, and with continuous reading of history, it came to possess for me a universal meaning so profound that it reached to the very roots of political action; so extended that it covered the whole.It is, indeed, a truth which explains and co-ordinates all one reads of human action in the past, and all one sees of it in the present. […] All tragedy is the conflict of a true right and a false right, or of a greater right and a lesser right, or, at the worst, of two false rights. Still more do men pretend in this time of ours, wherein the habitual use of the human intelligence has sunk to its lowest, that doctrine is but a private individual affair, creating a mere opinion. Upon the contrary, it is doctrine that drives the State; and every State is stronger in the degree in which the doctrine of its citizens is united. Nor have I met any man in my life, arguing for what should be among men, but took for granted as he argued that the doctrine he consciously or unconsciously accepted was or should be a similar foundation for all mankind. Hence battle.
And after this manner, Euclid, in the sixth book, mentions both excess and defect. But in the present problem he requires application...
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)
The Memsahib’s Quote of the Day https://survivalblog.com/the_memsahibs_quote_of_the_day_1/, Survivalblog, 5 May 2006
Letter III
The Nemesis of Faith (1849)
Context: The Mahometans say their Koran was written by God. The Hindoos say the Vedas were; we say the Bible was, and we are but interested witnesses in deciding absolutely and exclusively for ourselves. If it be immeasurably the highest of the three, it is because it is not the most divine but the most human. It does not differ from them in kind; and it seems to me that in ascribing it to God we are doing a double dishonour; to ourselves for want of faith in our soul's strength, and to God in making Him responsible for our weakness. There is nothing in it but what men might have written; much, oh much, which it would drive me mad to think any but men, and most mistaken men, had written. Yet still, as a whole, it is by far the noblest collection of sacred books in the world; the outpouring of the mind of a people in whom a larger share of God's spirit was for many centuries working than in any other of mankind, or who at least most clearly caught and carried home to themselves the idea of the direct and immediate dependence of the world upon Him. It is so good that as men looked at it they said this is too good for man: nothing but the inspiration of God could have given this. Likely enough men should say so; but what might be admired as a metaphor became petrified into a doctrine, and perhaps the world has never witnessed any more grotesque idol-worship than what has resulted from it in modern Bibliolatry. And yet they say we are not Christians, we cannot be religious teachers, nay, we are without religion, we are infidels, unless we believe with them. We have not yet found the liberty with which Christ has made us free. Infidels, Arthur! Ah, it is a hard word! The only infidelity I know is to distrust God, to distrust his care of us, his love for us. And yet that word! How words cling to us, and like an accursed spell force us to become what they say we have become.