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

### From inside the book

Results 1-5 of 35

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**Congruent**Figures will probably detect its influence throughout . The short treatise " On Quadrilaterals ' will , it is hoped , be found interesting to those students who have mastered the previous exercises , and useful to teachers in ... Page 13

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**congruent**. Ex . 1. - Two quadrilaterals , ABCD and PQRS , have the sides AB , BC , CD respectively equal to the sides PQ , QR , RS , and the angles B and C respectively equal to the angles Q and R. Show that the quadrilaterals are ... Page 21

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**congruent**. The student would do well to learn the enunciation in the subjoined form : — If two triangles have the three sides of the one equal to the three sides of the other , each to each , then the triangles are identically equal ... Page 23

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**congruent**As , ADF , AEF , on opposite sides of a common base , AF , and such that superposition could be effected by turning either of them about that common base until it came into the plane containing the other . From this property ... Page 45

... radius ) ; and then to make a triangle FAG

... radius ) ; and then to make a triangle FAG

**congruent**with DCE ( by describing arcs with centres A and F , and radii CD and DE , respectively ) . B PROPOSITION 24. THEOREM . If two triangles have two Book I. Prop . 23 . 45.### 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...