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

### From inside the book

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**vertices**, as D , be within the other triangle ACB , produce AC , AD to E and F respectively . Then because AC is equal to AD , [ HYP . therefore the angle ECD is equal to the angle FDC ; [ I. 5 . But the angle ECD is greater than the ... Page 41

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**vertices**of a triangle is greater than half the sum of the sides . Ex . 29. — Enunciate and prove a similar theorem as regards a quadri- lateral . Can it be extended to other polygons ( figures with more sides than three ) ? The four ... Page 78

... triangles , having two given points as

... triangles , having two given points as

**vertices**. The set consists of two bencils , one of parallels and the other of con . current lines . PROPOSITION 42. PRoblem . To describe a parallelogram that shall 78 Euclid's Elements . Page 102

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**vertices**which it joins . 3d . The other two angles are equal . 4th . The axis divides it into two congruent triangles , with equal sides adjacent . 5th . The median lines meet on the axis , and are equally inclined to it . Again ... Page 111

... two given straight lines . Hence also , show that any number of equilateral triangles can be described with their

... two given straight lines . Hence also , show that any number of equilateral triangles can be described with their

**vertices**one on each of three given straight lines . Ex . 122 - O is a fixed point , On Solving Geometrical Problems . III.### 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...