New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 45
... inscribed in a circle when its extremities are in the circumference ; as the line AB , or В С. C A A B B 132. An Inscribed Angle is one which has its vertex in the circumference , and is formed by two chords ; as the angle ABC . 133 ...
... inscribed in a circle when its extremities are in the circumference ; as the line AB , or В С. C A A B B 132. An Inscribed Angle is one which has its vertex in the circumference , and is formed by two chords ; as the angle ABC . 133 ...
Page 55
... angles . THEOREM X. 160. An inscribed angle is measured by half the arc included between its sides . A Let BAD be an inscribed angle , whose sides include the arc BD ; then the angle BAD is measured by half of the arc B D. C First ...
... angles . THEOREM X. 160. An inscribed angle is measured by half the arc included between its sides . A Let BAD be an inscribed angle , whose sides include the arc BD ; then the angle BAD is measured by half of the arc B D. C First ...
Page 56
... angle is measured by the half of the arc included between its sides . D 161. Cor . 1. All the angles , A E BAC , BDC , inscribed ... angle , BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi ...
... angle is measured by the half of the arc included between its sides . D 161. Cor . 1. All the angles , A E BAC , BDC , inscribed ... angle , BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi ...
Page 61
... angle ABC , being inscribed in a semicircle , is a right angle ( Theo . X. Cor . 2 , Bk . III . ) . X PROBLEM V. At a point in a given straight line to make an angle equal to a given angle Let A be the given point , A B the given line ...
... angle ABC , being inscribed in a semicircle , is a right angle ( Theo . X. Cor . 2 , Bk . III . ) . X PROBLEM V. At a point in a given straight line to make an angle equal to a given angle Let A be the given point , A B the given line ...
Page 65
... angle is a right angle , the figure will be a rectangle ; and if the adjacent sides are also equal , the figure will ... inscribed . PROBLEM XV . Through a given point to draw a tan- gent to a given circle . First . Let the given ...
... angle is a right angle , the figure will be a rectangle ; and if the adjacent sides are also equal , the figure will ... inscribed . PROBLEM XV . Through a given point to draw a tan- gent to a given circle . First . Let the given ...
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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.