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

### From inside the book

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**coincide**with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II . All right angles are equal to one another ... Page 12

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**coincide**with the point E , because AB is equal to DE ; [ HYP . And AC will fall on DF , because the angle BAC is equal to the angle EDF ; therefore also the point C will**coincide**with the point F , because AC is equal to DF ; [ HYP ... Page 13

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**coincides**with the whole triangle DEF , and is equal to it . [ AX . 8 . Also since AB , BC**coincide**with DE , EF , therefore the angle B is equal to the angle E. [ AX . 8 . And since AC , CB**coincide**with DF , FE , therefore the angle C ... Page 20

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**coinciding**with EF , BA and AC will**coincide**with ED and DF . For if not , on EF as base there will be another triangle formed on the same side of it as DEF , and having the side terminated at E equal to DE , and also the side ... Page 49

... D must lie somewhere on the straight line . from C through A , FLC ; .. it must

... D must lie somewhere on the straight line . from C through A , FLC ; .. it must

**coincide**with A , [ HYP . and .. the whole △ DEF**coincides**with the whole A ABC and = it , and AB = DE , and AC = DF , Book I. Prop . 26 . 49.### 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...