 In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.  Euclid in Greek - Side 236av Euclid - 1920 - 239 siderBegrenset visning - Om denne boken
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 440 sider
...BA. AF. Therefore the square on the side BF is equal to the squares on the sides BA, AF. Therefore in right-angled triangles the square on the side subtending...the squares on the sides containing the right angle. QED (Thomas [1939] 179, 181, 183, 185) 2.11 [constructing the proportion used in the Parthenon, which... | |
 | James Dale Williams - 2002 - 276 sider
...all, . . . French." Will Euclid do? Propositions 47 and 48 of Elements look like this: PROPOSITION 47 In right-angled triangles the square on the side subtending...the squares on the sides containing the right angle. PROPOSITION 48 If in a triangle the square on one of the sides be equal to the squares on the remaining... | |
 | Georg Wilhelm Friedrich Hegel - 2002 - 400 sider
...Hegels Entwicklung' (Stuttgart, 1936) pp. 288-300, 470-473. 228,29 Euclid's 'Elements' bk. I prop. 47, 'In right-angled triangles the square on the side...squares on the sides containing the right angle.' See the detailed account of the ways in which Pythagoras may have discovered this theorem in TL Heath... | |
 | Dick Teresi - 2010 - 468 sider
...sum of the squares of the other two sides. Note, by contrast, Euclid (Elements 147): "In right angled triangles the square on the side subtending the right...squares on the sides containing the right angle." To Euclid the Pythagorean theorem of right triangles meant literally that the square can be cut into... | |
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 440 sider
...is equal to the squares on the sides BA. AF. Therefore in right-angled triangles the square on die side subtending the right angle is equal to the squares on the sides containing the right angle. QED (Thomas [1939] 179, 181, 183, 185) 2.11 [constructing the proportion used in the Parthenon, which... | |
 | Audun Holme - 2002 - 408 sider
...Theorem". I.47 reads as follows, quoted from [16]: Pythagoras According to Euclid. In right angled triangles the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle. The parenthesis is tacitly assumed in... | |
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 438 sider
...[1939] 437, 439, 441, 443, 445) 1.47 ["Pythagoras' Theorem"] In right-angled triangles die square on die side subtending the right angle is equal to the squares on the sides containing die right angle, [known but never proved by Mesopotamians] Let ABF be a right-angled triangle having... | |
 | R. H. Warn, John G. Horner - 2002 - 292 sider
...cut off equal arcs. (Ene. III. 28.) (m) In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle. (Euc. I. 47.) USEFUL GEOMETRICAL PROBLEMS. 85.... | |
 | Chris Pritchard - 2003 - 572 sider
...construct, in a given rectilineal angle, a parallelogram equal to a given rectilineal figure. Prop. 47: In right-angled triangles the square on the side subtending...the squares on the sides containing the right angle. Prop. 48: If in a triangle the square on one of the sides be equal to the squares on the remaining... | |
 | Jean Christianidis - 2004 - 502 sider
...theorem of Pythagoras 1.47 as a generally stated premise which reads as follows (transl. by TL Heath): “In right-angled triangles the square on the side...squares on the sides containing the right angle”. Babylonian scribes knew how to use mathematical knowledge corresponding to general premises such as... | |
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