Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 29
... distances from the foot of the per- pendicular from the given point , are equal . 2. Theorem . Two equal oblique lines drawn from a point to a line meet it at equal distances from the foot of the perpen- dicular . PROPOSITION XVIII ...
... distances from the foot of the per- pendicular from the given point , are equal . 2. Theorem . Two equal oblique lines drawn from a point to a line meet it at equal distances from the foot of the perpen- dicular . PROPOSITION XVIII ...
Page 31
... distances QE and QH are unequal . For , suppose that one of these distances , as QE , cuts the bisector in some point P ; from P let PF be drawn perpen- dicular to AC , and join QF . We have QH < QF ; also QF < QP + PF , or QF < QP + PE ...
... distances QE and QH are unequal . For , suppose that one of these distances , as QE , cuts the bisector in some point P ; from P let PF be drawn perpen- dicular to AC , and join QF . We have QH < QF ; also QF < QP + PF , or QF < QP + PE ...
Page 33
... distances from the foot of the perpendicular , the more remote is the greater . 1st . If the lines lie on the same side of the perpendicular . Let PC be the perpendicular and PD and PE the two oblique lines , EC being greater than DC ...
... distances from the foot of the perpendicular , the more remote is the greater . 1st . If the lines lie on the same side of the perpendicular . Let PC be the perpendicular and PD and PE the two oblique lines , EC being greater than DC ...
Page 41
... distance between them the altitude of the trapezoid . 3d . The parallelogram ( C ) , which is bounded by two pairs of parallel sides . The side upon which a parallelogram is B A supposed to stand and the opposite side are called its ...
... distance between them the altitude of the trapezoid . 3d . The parallelogram ( C ) , which is bounded by two pairs of parallel sides . The side upon which a parallelogram is B A supposed to stand and the opposite side are called its ...
Page 53
... distance is laid off on a side of the parallelogram , care being taken that no two distances are laid off on the same side , the points thus obtained will be the vertices of a new parallelogram . 37. If from two opposite vertices of a ...
... distance is laid off on a side of the parallelogram , care being taken that no two distances are laid off on the same side , the points thus obtained will be the vertices of a new parallelogram . 37. If from two opposite vertices of a ...
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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.