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Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ...
No preview available - 2018
adding alternate altitude angle ACB base bisects the angle Book centre chord circle circumference common consequently construction contained describe a circle diagonals diameter difference distance divided double draw drawn equal EXERCISE extremities figure four given circle given line given point greater half harmonically hence hypotenuse intersection join less Let ABC line joining lines drawn manner meet middle opposite sides Pages parallel parallelogram pass perpendicular Price PROBLEM produced proportional proved quadrilateral radius ratio rectangle remains required locus required to prove respectively right angles right-angled triangle segments similar square straight line tangent third touch triangle triangle ABC twice vertex vertical angle whence wherefore Wood-cuts
Page 72 - ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC.
Page 55 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 26 - Prove that three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares on the lines drawn from the vertices to the middle points of the opposite sides.
Page 73 - If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x± b с bb Or °r
Page 58 - EH parallel to AB or DC, and through F draw FK parallel to AD or BC ; therefore each of the figures, AK, KB, AH, HD, AG, GC, BG...
Page 29 - The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals...
Page 24 - If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other side.