Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key


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Pagina 78 - ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC.
Pagina 25 - 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.
Pagina 61 - 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.
Pagina 32 - 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.
Pagina 79 - 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. = ^xĪ b с bb Or įr
Pagina 64 - 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...
Pagina 35 - The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals...
Pagina 4 - The perpendicular is the shortest straight line which can be drawn from a given point to a given straight line; and of others that which is nearer to the perpendicular is less than the more remote, and the converse; and not more than two equal straight lines can be drawn from the given point to the given straight line, one on each side of the perpendicular.
Pagina 30 - 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.
Pagina 8 - 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.

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