The Thirteen Books of Euclid's Elements ; The Works of Archimedes, Including the Method ; Introduction to Arithmetic |
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Page 305
... plane of reference . But the plane of reference is the plane through the straight lines AB , CD . Therefore FE is at right angles to the plane through AB , CD . Therefore etc. Q. E. D. PROPOSITION 5 If a straight line be set up at right ...
... plane of reference . But the plane of reference is the plane through the straight lines AB , CD . Therefore FE is at right angles to the plane through AB , CD . Therefore etc. Q. E. D. PROPOSITION 5 If a straight line be set up at right ...
Page 309
... plane with it are parallel to one another ; [ XI . 9 ] therefore AD is parallel and equal to CF. And AC , DF join ... reference the given plane ; thus it is required to draw from the point A a straight line perpendicular to the plane of ...
... plane with it are parallel to one another ; [ XI . 9 ] therefore AD is parallel and equal to CF. And AC , DF join ... reference the given plane ; thus it is required to draw from the point A a straight line perpendicular to the plane of ...
Page 314
... plane . [ XI . Def . 4 ] And FG , drawn in one of the planes DE at right angles to CE , the common section of the planes , was proved to be at right angles to the plane of reference ; therefore the plane DE is at right angles to the plane ...
... plane . [ XI . Def . 4 ] And FG , drawn in one of the planes DE at right angles to CE , the common section of the planes , was proved to be at right angles to the plane of reference ; therefore the plane DE is at right angles to the plane ...
Common terms and phrases
added apotome applied axis base called centre of gravity circle circle ABCD circumference circumscribed commensurable in length commensurable in square common cone constructed continued cube cylinder described diameter difference divided double draw drawn equal extremes fall figure fluid follows four fourth given greater half height Hence incommensurable inscribed joined least less magnitudes mean measure medial meet multiplying namely parallel parallelogram perpendicular placed plane polygon portion possible prime prism produced Prop proportional PROPOSITION proved pyramid ratio rational straight line reason rectangle remaining respectively right angles segment side similar Similarly solid sphere square number squares on AC straight lines commensurable surface taken third touch triangle twice the rectangle unit vertex whole