## The Harpur Euclid: An Edition of Euclid's Elements |

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The Harpur Euclid: An Edition of Euclid's Elements - Primary Source Edition Edward Mann Langley No preview available - 2013 |

### Common terms and phrases

ABCD base bisect bisector Book called centre chord circum-circle circumference coincide common constant construction contained converse demonstration described diagonals diameter distance divided draw drawn equal equilateral Euclid exercise external falls figure fixed four given circle given point given straight line greater Hence Ilgm inscribed internal intersect Join length less lies locus magnitude mean meet method mid-point NOTE opposite sides parallel parallelogram pass perpendicular plane problem produced Prop proportional PROPOSITION prove quadrilateral radius ratio rect rectangle contained rectilineal figure regular reqd respectively right angles segment Show shown sides similar Similarly square student Take taken tangent THEOREM third touch triangle ABC twice vertex vertices whole

### Popular passages

Page 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 369 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 390 - ... figures are to one another in the duplicate ratio of their homologous sides.

Page 97 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 40 - Any two sides of a triangle are together greater than the third side.

Page 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.

Page 407 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 156 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...