## The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope |

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### Common terms and phrases

adjacent angle contained angle equal base bc bcd Prop bisect coincide Const Const.—From Const.—In Const.—Join Const.—Let Demonst.—Because Demonst.—For demonstration diam diameter draw ebcf Enun Enun.—If Enun.—Let abc Enun.—To describe equal sides equilateral Euclid EUCLID'S ELEMENTS exterior exterior angle four rt given point given straight line Hence interior and opposite interior opposite isosceles isosceles triangle klmn KLNc Let abc line be drawn line drawn meet opposite angles opposite sides parallel parallelogram perpendicular Post PROB produced Proposition proved rectilineal figure rhombus right angles side bc square subtraction take any pt THEOR Theorem trapezium abcd vertical Wherefore XXIX XXXI XXXII XXXIV XXXVIII Zs Prop

### Popular passages

Page 60 - 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. either the sides adjacent to the equal...

Page 24 - 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, equal to one another.

Page 36 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Page 6 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Page 111 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.

Page 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.

Page 101 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 51 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Page 106 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Page 6 - 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.