## Elements of Geometry: Containing the First Six Books of Euclid with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical Trigonometry |

### From inside the book

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**join**FC , GB . A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles , AFC , AGB ; therefore the base FC is equal ... Page 15

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**join**DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore ... Page 17

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**join**DE , and upon it describe ( 1. 1. ) an equilateral triangle DEF ; then**join**AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF ... Page 18

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**join**FC ; the straight line FC , drawn from the giv- en point C , is at right angles to the given straight line AB . A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal to ... Page 20

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**join**BE and produce it to F , and make EF equal to BE ;**join**also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle CEF ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle BCD base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB produced PROP proportional proposition radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line AC tangent THEOR touches the circle triangle ABC triangle DEF wherefore

### Popular passages

Page 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 81 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.

Page 14 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall be equal.

Page 19 - The angles which one straight line makes with another upon one side uf it, are, either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.

Page 52 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C. Then the squares on AB, BC shall be equal to twice the rectangle AB, BC, together with the square on A C.

Page 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Page 242 - 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 9 - 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 119 - Reciprocal figures, viz. triangles and parallelograms, " are such as have their sides about two of their " angles proportionals in such a manner, that a side

Page 72 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...