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

### From inside the book

Results 1-5 of 52

Page 172

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**touch**one another which meet , but do not cut another . If each of two circles which**touch**each other is outside the other , they are said to**touch**each other externally ; if one is wholly within the other , they are said to**touch**... Page 173

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**touch**one another internally they shall not have the same centre . Let the Os ABC , CDE**touch**one another internally at C , they shall not have the same centre . A D E B Find F , the centre of the inner OCDE ; join FC , draw FE any ... Page 180

... two Os and join KA , KB , KC . Then rad . KA = rad . KB = rad . KC , .. K is the centre of the other O , which is impossible . [ III . 9 . [ III . 5 . PROPOSITION 11 . If two circles

... two Os and join KA , KB , KC . Then rad . KA = rad . KB = rad . KC , .. K is the centre of the other O , which is impossible . [ III . 9 . [ III . 5 . PROPOSITION 11 . If two circles

**touch**each other internally 180 Euclid's Elements . Page 181

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**touch**each other internally the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two Os ABC , ADE**touch**each other internally at the pt . A ; the st . line through their ... Page 182

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**touch**one another externally the straight line which joins their centres shall pass through the point of contact . Let the two Os ABC , ADE**touch**each other externally at the pt . A ; the join of their centres shall pass through A. E DA ...### 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...