## New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |

### From inside the book

Results 1-5 of 13

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**equal**to CF ; and in like manner it may be shown that A D is**equal**to DF . Therefore A C , the**half**of the line A C F , is shorter than AD , the**half**of the line A D F ; hence the oblique line which meets the given line the greater ... Page 55

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**measured by half**the arc included between its sides . Let BAD be an inscribed angle , whose sides include the arc BD ; then the angle B A D is**measured by half**of the arc B D. First . Suppose the center ... measured by the half BOOK III . 55. Page 56

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**measured**by the**half**of BE minus the**half**of ED , or by the**half**of B D. Hence every inscribed angle is**measured**by the**half**of the arc included between its sides . 161. Cor . 1. All the angles , BAC , BDC , inscribed in the same segment , ... Page 57

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**measured by half**the circumference ; hence their sum is equal to two right angles . THEOREM XI . 165. The angle formed by the intersection of two chords is**measured by half**the sum of the two ... half of A MD , plus the half of BOOK III . 57. Page 58

... half of A MD , plus the half of DC ; or by half the whole arc AMD C. In like manner , it may be shown that the angle CAE is

... half of A MD , plus the half of DC ; or by half the whole arc AMD C. In like manner , it may be shown that the angle CAE is

**measured by half**the intercepted arc A C. THEOREM XIII . 167. The angle formed by two secants is**measured by half**...### Other editions - View all

### Common terms and phrases

A B C D ABCD ABCDEF alti altitude altitude Theo angle A CD axis base multiplied bisect chord circumference circumscribed cone convex surface diagonal diameter divided Elementary Algebra ellipse entire surface equal Theo equivalent frustum greater GREENLEAF'S NEW MATHEMATICAL Greenleaf's New Series half the sum hence homologous homologous sides hypothenuse inches inscribed circle magnitudes MATHEMATICAL SERIES mean proportional measured by half number of sides parallelogram parallelopipedon Parker's Exercises perimeter perpendicular prism PROBLEM radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo rods Scholium School secant line side A B side B C similar slant hight solid sphere is equal spherical square described square feet THEOREM triangles A B C triangular triangular prism vertex zoid

### 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.