## Elements of Geometry, Part 1 |

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ABCD altitude apply base bisector bisects called centre chord circle circumference circumscribed coincide common construct contains conversely corresponding describe diagonals diameter difference distance divided draw drawn equal equation equilateral triangle equivalent Exercise external extremities fall figure Find four GEOMETRY given given straight line GIVEN—the greater half Hence hypotenuse included inscribed intersection isosceles length less limit line joining locus mean proportional measured meet method middle points opposite sides parallel parallelogram passes perpendicular polygon position PROBLEMS PROPOSITION PROVE quadrilateral quantity radii radius ratio ratio of similitude rect rectangle regular polygon right angles right triangle segments sides similar square straight line Substituting tangent THEOREM third side triangle ABC triangle is equal turns unequal unit vertex vertices

### Popular passages

Page 44 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 65 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 143 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.

Page 61 - 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. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.

Page 146 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.

Page 54 - Two oblique lines cutting off equal distances from the foot of the perpendicular are equal.

Page 44 - If two triangles have two sides of one equal respectively to two sides of the other...

Page 98 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.

Page 125 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 179 - The areas of two similar triangles are to each other as the squares of any two homologous sides.