Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 65
... unit . Thus , to measure a line is to find the number expressing how many times it contains another line , called the unit of length , or the linear unit . The number which expresses how many times a quantity contains the unit is called ...
... unit . Thus , to measure a line is to find the number expressing how many times it contains another line , called the unit of length , or the linear unit . The number which expresses how many times a quantity contains the unit is called ...
Page 66
... unit ( 28 ) . It is implied in the defini- tion of ratio that the quantities compared are of the same kind . Hence , also , instead of the definition ( 28 ) , we may say that to measure a quantity is to find its ratio to the unit . The ...
... unit ( 28 ) . It is implied in the defini- tion of ratio that the quantities compared are of the same kind . Hence , also , instead of the definition ( 28 ) , we may say that to measure a quantity is to find its ratio to the unit . The ...
Page 68
... unit FD , by the numbers 17 and 5 ; and their 17 ratio is 5 33. When the preceding process is applied to two quanti- ties and no remainder can be found which is exactly con- tained in a preceding remainder , however far the process be ...
... unit FD , by the numbers 17 and 5 ; and their 17 ratio is 5 33. When the preceding process is applied to two quanti- ties and no remainder can be found which is exactly con- tained in a preceding remainder , however far the process be ...
Page 75
... unit of angle is the angle at the centre which intercepts the adopted unit of arc . Let AOB be an angle at the centre O , and AB its intercepted arc . Let AOC be the angle which is adopted as the unit of angle , and let its intercepted ...
... unit of angle is the angle at the centre which intercepts the adopted unit of arc . Let AOB be an angle at the centre O , and AB its intercepted arc . Let AOC be the angle which is adopted as the unit of angle , and let its intercepted ...
Page 76
... unit of angle ; nevertheless custom has sanctioned a different unit . The unit of angle generally adopted is an angle equal to part of a right angle , called a degree , and denoted by the symbol . The corresponding unit of arc is part ...
... unit of angle ; nevertheless custom has sanctioned a different unit . The unit of angle generally adopted is an angle equal to part of a right angle , called a degree , and denoted by the symbol . The corresponding unit of arc is part ...
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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.