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

### From inside the book

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Page 203

... be described to pass through A , E , O , D. Show angle AED = twice angle ABD = angle AOD . Show also that B , E , O , C are

... be described to pass through A , E , O , D. Show angle AED = twice angle ABD = angle AOD . Show also that B , E , O , C are

**concyclic**. PROPOSITION 22. THEOREM . The opposite angles of any quadrilateral Book III . Prop . 21 . 203. Page 206

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**concyclic**. ( Compare Ex . 326. ) Ex . 336. — If a cyclic quadrilateral have two sides parallel , it must have the other two sides equally inclined to the parallels . State and prove the converse theorem . Ex . 337. - If a cyclic ... Page 228

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**concyclic**. Ex . 378. - Deduce III . 36 , Cor . ( i . ) , from III . 35 . Ex . 379. - In equiangular triangles , the rectangles contained by the non - corresponding sides about equal angles are equal . Let ABC , AB'C ' be equiangular ... Page 232

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**concyclic**. Ex . 402. - On any three straight lines TA , TB , TC , drawn from the same point T , as diameters are described circles which intersect again in P , Q , R. If AP , BQ pass through T , show that CR also passes through T. ( P ... Page 236

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**concyclic**. Join AB and use III . 32 . Ex . 442. — ACB , ADB are two intersecting circles ; AC , AD are tangents to ADB , ACB at A. Show that ABC = LABD . Use III . 32 . L Ex . 443. - AB , BC , CD are three equal chords of a circle ABCD ...### 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...