New Elementary Geometry: With Practical Applications : a Shorter Course Upon the Basis of the Larger WorkRobert S. Davis & Company, 1874 - 176 páginas |
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Página 25
... consequently they are parallel ( Art . 14 ) . THEOREM XVI . 62. If a straight line , intersecting two other straight lines , makes any exterior angle equal to the interior and opposite angle , or makes the interior angles on the same ...
... consequently they are parallel ( Art . 14 ) . THEOREM XVI . 62. If a straight line , intersecting two other straight lines , makes any exterior angle equal to the interior and opposite angle , or makes the interior angles on the same ...
Página 32
... consequently AD is parallel to BC ( Theo . XV . ) ; there- fore the figure ABCD is a parallelogram . THEOREM XXV . 84. The diagonals of every parallelogram bisect each other , or divide each other into equal parts . Let ABCD be a ...
... consequently AD is parallel to BC ( Theo . XV . ) ; there- fore the figure ABCD is a parallelogram . THEOREM XXV . 84. The diagonals of every parallelogram bisect each other , or divide each other into equal parts . Let ABCD be a ...
Página 47
... consequently divides the circle into two equal parts ; hence the surface AFC is equal to the surface AFCB , a part to the whole , which is impossible . 140. Cor . 2. The arc of a circle , F E 43 C B whose chord is a diameter , is a semi ...
... consequently divides the circle into two equal parts ; hence the surface AFC is equal to the surface AFCB , a part to the whole , which is impossible . 140. Cor . 2. The arc of a circle , F E 43 C B whose chord is a diameter , is a semi ...
Página 66
... consequently is a tangent ( Theo . VII . Bk . III . ) . In like manner it be shown that E B is a tangent . may EXERCISES FOR ORIGINAL THOUGHT , ON REVIEW . 170. 1. The diameter is the longest straight line that can be inscribed in a ...
... consequently is a tangent ( Theo . VII . Bk . III . ) . In like manner it be shown that E B is a tangent . may EXERCISES FOR ORIGINAL THOUGHT , ON REVIEW . 170. 1. The diameter is the longest straight line that can be inscribed in a ...
Página 70
... consequently equal ( Theo . XIII . Bk . I. ) . If from the quadrilateral A B E D , we take away the tri- angle A D F , there will remain the parallelogram ABEF ; and if from the same quadrilateral A BED , we take away the triangle CB E ...
... consequently equal ( Theo . XIII . Bk . I. ) . If from the quadrilateral A B E D , we take away the tri- angle A D F , there will remain the parallelogram ABEF ; and if from the same quadrilateral A BED , we take away the triangle CB E ...
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD ABCDEF alti altitude Theo angle A CD axis base multiplied bisect chord circum circumference circumscribed cone convex surface D E F diagonal diameter divided ELEMENTARY ALGEBRA ellipse entire surface equal Theo equivalent formed frustum greater GREENLEAF'S half the sum hence homologous homologous sides hypothenuse inches inscribed circle inscribed square intersection magnitudes mean proportional measured by half Metric System number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo right pyramid rods Scholium SCHOOLS sector semicircle side A B side B C similar slant hight solid sphere is equal spherical square described square feet square root tangent THEOREM third triangles A B C triangular triangular prism tude vertex
Pasajes populares
Página 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Página 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Página 93 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Página 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Página 88 - FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.
Página 124 - But the solidity of each triangular prism is equal to the product of its base by its altitude ; and.