## The Elements of Plane Geometry ...W.S. Sonnenschein and Company, 1884 - Geometry, Modern |

### From inside the book

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Page 110

... rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the ...

... rectangle contained by the whole line and one of the parts is equal to the sum of the square on that part and the ...

**twice the rectangle**contained by them . Let AB , BC , be the two lines , and let them be placed so that AC is their sum ... Page 111

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**twice the rectangle**contained by AB and BC . Upon AC describe the square ADEC , and upon AB , BC describe the ... rectangle contained by GF , FD , is also that contained by AB , BC ; and HE , being the rectangle contained by EK , KH , is ... Page 112

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**twice the rectangle**contained by AB and BC . Q.E.D. COR . The square on a line , which is divided internally into two segments , is greater than the sum of the squares on the segments by**twice the rectangle**contained by them . Ex . 14 ... Page 113

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**twice the rectangle**contained by AB and BC . Upon AC describe the square ADEC , and upon AB , BC describe the ... rectangle contained by FG , FD , is also that contained by AB , BC ; and HE , being the rectangle contained by EK , KH , is ... Page 119

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**twice the rectangle**contained by either side and the projection on it of the other side . Let ABC be a triangle having the angle BAC an obtuse angle , and let CD be perpendicular to BA produced : A B then shall the square on BC be ...### Other editions - View all

### Common terms and phrases

AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisectors bisects centre circle cutting Constr construct a triangle contrapositive diagonal equal angles equal to AC exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral radius rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC side DF sides equal square on AC squares on AB straight angle straight line drawn Theorem trapezium triangle ABC triangle DEF triangles are identically twice the rectangle vertex

### Popular passages

Page 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 70 - 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 56 - ... is equal to twice as many right angles as the polygon

Page 101 - Prove that parallelograms on the same base and between the same parallels are equal in area.

Page 35 - Any two sides of a triangle are together greater than the third side.

Page 26 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.

Page 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 85 - The locus of a point at a given distance from a given point is the circumference described from the point with the given distance as radius.

Page 42 - 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 110 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.