Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 14
... lines in the same plane which will not meet , however far produced — are parallel . TRIANGLES . 6. Definitions . A plane triangle is a portion of a plane bounded by three intersecting straight lines ; as ABC . The sides of the triangle ...
... lines in the same plane which will not meet , however far produced — are parallel . TRIANGLES . 6. Definitions . A plane triangle is a portion of a plane bounded by three intersecting straight lines ; as ABC . The sides of the triangle ...
Page 15
... sides DE and DF are equal , the third side EF is always called the base . When any side BC of a triangle has been adopted as the base ... Parallel lines have the same direction . PROPOSITION I. - THEOREM . 10. At a given point BOOK I. 15.
... sides DE and DF are equal , the third side EF is always called the base . When any side BC of a triangle has been adopted as the base ... Parallel lines have the same direction . PROPOSITION I. - THEOREM . 10. At a given point BOOK I. 15.
Page 34
William Chauvenet. 2d . If the lines lie on opposite sides of the perpendicular . Let PC be the perpendicular and PD and PE the oblique lines , EC being greater than CD ... line AD , are parallel , by Proposition 34 ELEMENTS OF GEOMETRY .
William Chauvenet. 2d . If the lines lie on opposite sides of the perpendicular . Let PC be the perpendicular and PD and PE the oblique lines , EC being greater than CD ... line AD , are parallel , by Proposition 34 ELEMENTS OF GEOMETRY .
Page 35
... Lines having the same direction are parallel . Suggestion . Suppose them to meet ; v . Postulate II . 2. Theorem . - Lines parallel to the same line are parallel to each other . 43. Definitions . When two straight lines AB , CD , are ...
... Lines having the same direction are parallel . Suggestion . Suppose them to meet ; v . Postulate II . 2. Theorem . - Lines parallel to the same line are parallel to each other . 43. Definitions . When two straight lines AB , CD , are ...
Page 36
... lines are parallel . Let the line AB cut the lines CD and EF , making the alternate - interior angles CAB and ABF equal ; then are CD and EF parallel . Through G , the middle point of AB , draw GH per- pendicular to CD , and cut- ting ...
... lines are parallel . Let the line AB cut the lines CD and EF , making the alternate - interior angles CAB and ABF equal ; then are CD and EF parallel . Through G , the middle point of AB , draw GH per- pendicular to CD , and cut- ting ...
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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.