A lot of points please help. Questions above and article below. by his student. And so I come to one example that has given me a great 45 deal of unease and exemplifies many of the problems that have uncovered in Ptolemyoh, that I could sit down with that mind and show him the wonders we have discovered since his lifetime! how he would marvel! how much more than I would he be able to infer! -namely, the ratios of the 50 sun, earth, and moon. By calculating the radii of the sun, earth, and moon, Ptolemy was able to determine the ratios of their diameters. "Therefore," saith he, "where the moon's diameter is 1, the earth's diameter will be about 3, and the sun's 18. Therefore the carth's diameter is 3 times the 55 moon's and the sun's diameter is 18 times the moon's and 5 times the earth's. " He makes this claim as a step in the work of deriving the ratios of the volumes of the sun, earth, and moon; but before we proceed, let us pause. The moon's mean radius is only about 1,700 kilometers, 60 smaller than it would need to be to comprehension one third of carth. In fact, the radius of the moon is only slightly above a quarter of the radius of the earth, making the ratio of their diameters much closer to 1: 4 instead of 1: 3. Furthermore, the sun, we now understand, is on a scale far vaster than 65 that of the earth; it might be something like twenty, fifty, eighty, or one hundred times the size of the earth. If future measurements are based on these flawed ratios, almost none of the volumes in the text can be correct. The following is excerpted from Observations and Notes by the medieval astronomer Hans Schrenk (1455-1507), translated by Prof. Renata Muller in 1973. On finding that Prolemy's conception of the heavenly bodies was credited among my students and indeed among many of my peers as a creditable attempt to describe the motion and sizes of sun, moon, and planets, I resolved to 5 undertake a review of his great work Almagest in treating it with the skepticism I should use to read a treatise published today; and therefore I settled down with the observations and calculations to verify the mathematics and see once and for all whether they held true. I found at once that 10 many Ptolemaic assumptions were based upon universal principles held by Aristotle who, though a very great thinker, was a philosopher rather than a mathematician. In short, I was often subject to the sense that Ptolemy valued Aristotelian tenets more strongly than numerical outcomes 15 and attempted to siphon the math into the philosophy. Everything in Ptolemy's calculation came out just a little too roundly. It was quickly apparent that slight infelicities in the mathematics produced philosophically satisfying numbers that may not, in fact, reflect the reality of the size, volume, speed, orbits, or direction of the moving bodies. Thus affirmed in the validity of my suspicion of Ptolemy, I stayed up nights and worked, leaf by leaf, through every one of his claims. It is not out of the desire to disprove a long-accepted 25 theory or to elevate myself as the one who revealed a charlatan or, worse to my mind, pointed out an embarrassing error made by one greater than myself that I chose to check the calculations of Ptolemy. Were it not for his masterful and extremely detailed record of his observations, sources, 30 and proofs, the field of astronomy would not be as advanced as it is today. Notwithstanding the mistaken assumptions, the Almagest is indeed one of the greatest works of mathematical astronomy that we possess, and it is only because of its greatness and its essential nature to the future 35 growth of our scientific knowledge that it can withstand such a close scrutiny as I paid to it between the months of August and November nearly nightly. Far from vaunting myself up as the "discoverer" of the cracks and flaws in Ptolemy, I come to him as student to a master who has 40 taken home a proof that he could never have invented and found a slightly more efficient way to solve it : it makes the master all the greater to be so minutely checked and honed