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### Innhold

 FIRST BOOK PAGE 1 SECOND BOOK 27 FOURTH BOOK 55
 SIXTH BOOK 69 GEOMETRICAL MAXIMA AND MINIMA 93 PORISMS 106

### Populĉre avsnitt

Side 72 - ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC.
Side 19 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Side 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.
Side 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.
Side 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. = ^xħ b с bb Or °r
Side 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...
Side 29 - The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals...
Side 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.
Side 2 - Of all triangles having the same vertical angle, and whose bases pass through a given point, the least is that whose base is bisected in the given point.