Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 10
... describe the line . By the direction of a line at any point we mean the direc- tion in which a point describing the line is moving when it passes through the point in question . Definitions . A straight line is a line which has ...
... describe the line . By the direction of a line at any point we mean the direc- tion in which a point describing the line is moving when it passes through the point in question . Definitions . A straight line is a line which has ...
Page 13
... describe , or to generate , the angle AOB . By con tinuing the revolution , an angle of any magnitude may be generated . 4. Definitions . When one straight line meets another , so as to make two adjacent angles equal , each of these ...
... describe , or to generate , the angle AOB . By con tinuing the revolution , an angle of any magnitude may be generated . 4. Definitions . When one straight line meets another , so as to make two adjacent angles equal , each of these ...
Page 55
... describe a circumference , whose radii are all equal to OA . 2. Definitions . An arc of a circle is any portion of its cir- cumference ; as DEF . A chord is any straight line joining two points of the cir- cumference ; as DF . The arc ...
... describe a circumference , whose radii are all equal to OA . 2. Definitions . An arc of a circle is any portion of its cir- cumference ; as DEF . A chord is any straight line joining two points of the cir- cumference ; as DF . The arc ...
Page 82
... describe arcs intersecting in the two points D and E. Through these points draw the straight line DE , which bisects AB at the point C. For , D and E being equally distant from A and B , the straight line DE is perpendicular to AB at ...
... describe arcs intersecting in the two points D and E. Through these points draw the straight line DE , which bisects AB at the point C. For , D and E being equally distant from A and B , the straight line DE is perpendicular to AB at ...
Page 83
... describe two arcs intersecting in F. Then CF is the required perpendicular ( I. , Proposition XVIII . ) . 57. Another solution . Take any point O , without the given line , as a centre , and with a radius equal to the distance from 0 to ...
... describe two arcs intersecting in F. Then CF is the required perpendicular ( I. , Proposition XVIII . ) . 57. Another solution . Take any point O , without the given line , as a centre , and with a radius equal to the distance from 0 to ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.