New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 25
... consequently they are parallel ( Art . 14 ) . THEOREM XVI . 62. If a straight line , intersecting two other straight linés , 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 linés , makes any exterior angle equal to the interior and opposite angle , or makes the interior angles on the same ...
Page 32
... consequently A D 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 A D 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 ...
Page 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 , A F E 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 , A F E C B whose chord is a diameter , is a semi ...
Page 66
... consequently is a tangent ( Theo . VII . Bk . III . ) . In like manner it may be shown that E B is a tangent . 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 may be shown that E B is a tangent . EXERCISES FOR ORIGINAL THOUGHT , ON REVIEW . 170. 1. The diameter is the longest straight line that can be inscribed in a ...
Page 70
... consequently equal ( Theo . XIII . Bk . I. ) . If from the quadrilateral A BED , we take away the tri- angle ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral A BED , we take away the triangle CBE ...
... consequently equal ( Theo . XIII . Bk . I. ) . If from the quadrilateral A BED , we take away the tri- angle ADF , there will remain the parallelogram ABEF ; and if from the same quadrilateral A BED , we take away the triangle CBE ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 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.
Page 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.
Page 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.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 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.
Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 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...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.