Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 15
... drawn . Postulate II . Through a given point one straight line , and only one , 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 ...
... drawn . Postulate II . Through a given point one straight line , and only one , 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 ...
Page 28
... drawn through P. Let PC in the figure below be this perpendicular . No other perpendicular from P can be drawn to the line AB . For , suppose that a second perpendicular PD could be drawn . Extend PC to P ' , making CP ' equal to PC ...
... drawn through P. Let PC in the figure below be this perpendicular . No other perpendicular from P can be drawn to the line AB . For , suppose that a second perpendicular PD could be drawn . Extend PC to P ' , making CP ' equal to PC ...
Page 29
... drawn from P to AB , that assumption must be false . EXERCISES . 1. Theorem . A perpendicular let fall from the vertex of an isosceles triangle upon the base bisects the base and bisects the vertical angle . 2. Theorem . - Two right ...
... drawn from P to AB , that assumption must be false . EXERCISES . 1. Theorem . A perpendicular let fall from the vertex of an isosceles triangle upon the base bisects the base and bisects the vertical angle . 2. Theorem . - Two right ...
Page 34
... drawn parallel to a given line . Let A be the given point and A E BC the given line . From A draw AD perpendicular B- to BC , and through A draw AE C perpendicular to AD . AE and DC , being perpendicular to the same line AD , are ...
... drawn parallel to a given line . Let A be the given point and A E BC the given line . From A draw AD perpendicular B- to BC , and through A draw AE C perpendicular to AD . AE and DC , being perpendicular to the same line AD , are ...
Page 36
... draw GH per- pendicular to CD , and cut- ting EF in I. Then the triangles AGH H A D G E- F B I and BGI , having the side AG equal to the side GB by construction , the angle GAH equal to the angle GBI by hypothesis , and the angle AGH ...
... draw GH per- pendicular to CD , and cut- ting EF in I. Then the triangles AGH H A D G E- F B I and BGI , having the side AG equal to the side GB by construction , the angle GAH equal to the angle GBI by hypothesis , and the angle AGH ...
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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.