## The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's Data |

### From inside the book

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**bisect**a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to**bisect**it . b Take any point D in AB , and from AC cut off AE equal to AD ; join DE , and upon ... Page 17

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**bisected**, it may be de- monstrated that the angle BCG , that is , the angle ACD is d 15. 1 . greater than the angle ABC . Therefore , " if one side , " & c . Q. E. D. d PROP . XVII . THEOR . Any two angles of a triangle are together ... Page 35

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**Bisect**BC in E , join AE , and at the point E in the straight a 10. 1 . line EC make the angle CEF equal to D ; and through A b 23. 1 . draw G parallel to BC , and c C through C draw CG parallel to EF : Therefore FECG is a parallelogram ... Page 47

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**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 of half the line**bisected**, is equal to the square of the straight line which is ... Page 51

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**bisected**, and of the square of the line made up of the half and the part produced . Let the straight line AB be**bisected**in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD . From the ...### Other editions - View all

The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |

### Common terms and phrases

ABCD altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore

### Popular passages

Page 95 - 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 153 - 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 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Page 11 - 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 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Page 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Page 26 - IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite, upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Page 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.