## The First Book of Euclid's Elements: Arranged for Beginners |

### Common terms and phrases

ABC is equal alternate angles angle ABC angle ACB angle BAC angle equal angles FAB angular point area of ABC base BC bisectors bisects the angle centre coincide Consider the triangles Construction corresponding angle DEF are equal describe a triangle describe the circle diagonal equal angles equal area equal in area equal respectively equal to CD equidistant equilateral triangle exterior angle finite straight line given angle given finite straight given point given straight line given triangle greater included angle interior opposite angle intersect isosceles triangle line BC middle point opposite sides parallelogram perpendicular plane Prop Proposition Q.E.D. EXAMPLES quadrilateral radius rectilineal figure required to prove rhombus right angles right-angled triangle Shew side BC sides equal square straight angle surface third side triangle ABC triangle DEF triangles are equal unlimited straight line Wherefore

### Popular passages

Page 28 - 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 72 - 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 48 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.

Page 155 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.

Page 118 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.

Page 153 - ... is equal to the sum of the areas of the squares on the other two sides.

Page 114 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 139 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 125 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.