## The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |

### From inside the book

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**Hence**every equilateral triangle is also equiangular . A corollary is a proposition , the truth of which follows immediately or may easily be deduced from what has been demonstrated in the proposition to which it is attached ... Page 16

... , which is absurd ; [ AX . 9 . therefore AB is not unequal to AC , that is , AB is equal to AC . COROLLARY . -

... , which is absurd ; [ AX . 9 . therefore AB is not unequal to AC , that is , AB is equal to AC . COROLLARY . -

**Hence**every equiangular triangle is also equilateral . NOTE . A theorem consists of two parts , the 16 Euclid's Elements . Page 27

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**Hence**the similarity between it and Prop . 9. As in Prop . 9 the demonstration would be just as easy if ACB were any isosceles △ having AB for its base ; and in Practical Geometry arcs with any equal radii long enough to ensure their ... Page 51

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**Hence**: - The locus of a point equidistant from two straight lines drawn from the same point is the bisector of the angle contained by them . For the same use of the word locus see Note on Ex . 8 . The following proposition is slightly ... Page 62

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**Hence**the truth of Cor . II . A rectilineal figure , which is equilateral and equiangular , is called regular , e.g. an equilateral △ is a regular figure . Ex . 49. - If a small st . line slide along the outside rectilineal path BPQRC ...### Other editions - View all

### Common terms and phrases

bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices

### 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...