Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 10
William Chauvenet. If a line is terminated , it is terminated by points . If two lines intersect , they intersect in ... given position , it must move in some definite direction ; if it continues to move in the same direction , its path is a ...
William Chauvenet. If a line is terminated , it is terminated by points . If two lines intersect , they intersect in ... given position , it must move in some definite direction ; if it continues to move in the same direction , its path is a ...
Page 11
... straight lines alone are called rectilinear , or right - lined , figures ; a straight line being often called a ... given con- ditions , of their measurement and of their properties . Plane geometry treats of plane figures . The ...
... straight lines alone are called rectilinear , or right - lined , figures ; a straight line being often called a ... given con- ditions , of their measurement and of their properties . Plane geometry treats of plane figures . The ...
Page 15
... can be drawn having any given direction . 9. Axiom I. A straight line is the shortest line that can be drawn between two points . Axiom II . Parallel lines have the same direction . PROPOSITION I. - THEOREM . 10. At a given point BOOK I.
... can be drawn having any given direction . 9. Axiom I. A straight line is the shortest line that can be drawn between two points . Axiom II . Parallel lines have the same direction . PROPOSITION I. - THEOREM . 10. At a given point BOOK I.
Page 16
... straight line one perpendicular to the line can be drawn , and but one . Let O be the given point in the line AB . Suppose a line OD , constantly passing through O , to revolve about O , starting from the position OA and stopping at the ...
... straight line one perpendicular to the line can be drawn , and but one . Let O be the given point in the line AB . Suppose a line OD , constantly passing through O , to revolve about O , starting from the position OA and stopping at the ...
Page 28
William Chauvenet. PROPOSITION XVI . - THEOREM . 32. From a given point , without a straight line , one perpen- dicular can be drawn to the line , and but one . Let AB be the given line and P the given point . Take a second line DE , and ...
William Chauvenet. PROPOSITION XVI . - THEOREM . 32. From a given point , without a straight line , one perpen- dicular can be drawn to the line , and but one . Let AB be the given line and P the given point . Take a second line DE , and ...
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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.