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

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### Common terms and phrases

ABC is equal ABCD adjacent angle ABC angle ACB angle BAC angle equal applied base base BC called centre circle coincide Consider the triangles Construction crosses describe diagonal difference direction distance draw equal in area equal respectively equal to BC equidistant equilateral triangle exterior angle fall figure finite straight line four geometrical given angle given finite straight given point given straight line greater half included angle indicate interior opposite angle intersect isosceles triangle length less Let ABC line joining lines drawn meet middle point opposite sides pair parallel parallelogram perpendicular plane portion position produced Proof Prop Proposition Q.E.D. EXAMPLES quadrilateral Question radius represent required to prove right angles Shew side BC sides equal solid square straight angle surface taken triangle ABC triangles are equal turning 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.