Geometrical Solutions Derived From Mechanics, a Treatise of Archimedes
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In our eReader you can find the full English version of the book. Read Geometrical Solutions Derived From Mechanics, a Treatise of Archimedes Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Geometrical Solutions Derived From Mechanics, a Treatise of Archimedes
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IO, structed on /?8 perpendicular to ay. Then imagine a cone whose base is the circle with the diameter /38, whose vertex is at a and its lateral boundaries are fta and a8 ; let ya be produced so that ad = ya, imagine the straight line By to be a scale-beam with its center at a and in the semi-circle fia.8 draw a straight line £0 1 1 (38 ; let it cut the circumference of the semicircle in | and o, the lateral boundaries of the cone in ir and p, and ay in c . On |o construct a plane perpen- dicu...lar to ae; it will intersect the hemisphere in a circle with the diameter £0, and the cone in a circle with the diameter m. Now because ay.ae = & 2 : ae 2 and £a 2 = ae 2 + e£ 2 and ae = ew, therefore ay : ae = £e 2 + en 2 : eTr 2 . But $e 2 + €ir 2 :€Tr 2 -the circle with the diameter £0 + the circle with the diameter irp : the circle with the diameter wp, and ya = a0, hence 6a : ae = the circle with the diameter |o + the circle with the diameter np : circle with the diameter irp.
Therefore the two circles whose diameters are £0 and irp in their present position are in equilibrium at the point a with the circle whose diameter is wp if it is transferred and so arranged at 6 that 6 is its center of gravity.
What to read after Geometrical Solutions Derived From Mechanics, a Treatise of Archimedes?
You can find similar books in the "Read Also" column, or choose other free books by Smith, David Eugene, 1860-1944 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
IO, structed on /?8 perpendicular to ay. Then imagine a cone whose base is the circle with the diameter /38, whose vertex is at a and its lateral boundaries are fta and a8 ; let ya be produced so that ad = ya, imagine the straight line By to be a scale-beam with its center at a and in the semi-circle fia.8 draw a straight line £0 1 1 (38 ; let it cut the circumference of the semicircle in | and o, the lateral boundaries of the cone in ir and p, and ay in c . On |o construct a plane perpen- dicu...lar to ae; it will intersect the hemisphere in a circle with the diameter £0, and the cone in a circle with the diameter m. Now because ay.ae = & 2 : ae 2 and £a 2 = ae 2 + e£ 2 and ae = ew, therefore ay : ae = £e 2 + en 2 : eTr 2 . But $e 2 + €ir 2 :€Tr 2 -the circle with the diameter £0 + the circle with the diameter irp : the circle with the diameter wp, and ya = a0, hence 6a : ae = the circle with the diameter |o + the circle with the diameter np : circle with the diameter irp.
Therefore the two circles whose diameters are £0 and irp in their present position are in equilibrium at the point a with the circle whose diameter is wp if it is transferred and so arranged at 6 that 6 is its center of gravity.
What to read after Geometrical Solutions Derived From Mechanics, a Treatise of Archimedes?
You can find similar books in the "Read Also" column, or choose other free books by Smith, David Eugene, 1860-1944 to read onlineMoreLess
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