## Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Part 1 |

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### Common terms and phrases

AB=DE ABCD AC=DF adjacent adjacent angles angle contained angles equal angular points base BC BC=EF centre coincide diagonal draw a straight equal angles equilat equilateral triangle Euclid Geometry given angle given point given st given straight line greater hypotenuse iBAC interior angles intersect isosceles triangle l s ABC lACB lBAC Let ABC Let the st lines be drawn magnitude meet middle points opposite angles opposite sides parallelogram perpendicular polygon Postulate produced Prop Proposition proved quadrilateral rectangle contained reqd rhombus right angles Shew shewn sides equal square sum of l s sum of sqq Take any pt Theorem together=two rt trapezium triangle ABC triangles are equal twice rect twice sq vertex vertical angle

### Popular passages

Page 52 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Page 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Page 83 - If a straight line be 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 made up of the half and the part produced.

Page 17 - 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 48 - 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 26 - 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 86 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 90 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...

Page 106 - 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 82 - 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.