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

### From inside the book

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**radii**of a circle are equal ; all the diameters are also equal , and each is double the radius . 124. An Arc of a circle is any part of the circumference ; as the part AD , A E , or E G F. 125. The Chord of an arc is the straight line ... Page 45

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**radii**drawn to the extremities of the arc ; as the surface included between the arc AD , and the two**radii**CA , CD . 128. A Secant to a circle is a straight line which cuts the circum- A ference in two points , and lies partly within ... Page 47

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**radii**CD , OG are drawn , the triangles ACD , E O G , having the three sides of the one equal to the three sides of the other , each to each , are themselves equal ( Theo . XIII . Bk . I. ) ; therefore the angle A CD is equal to the an ... Page 48

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**radii**CA , CD , and CB . The two sides AC , CB in the triangle A CB are equal to the two A C , C D in the triangle ACD , and the angle ACB is greater than the angle A CD ; therefore the third side A B is greater than the third side AD ... Page 49

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**radii**which make equal angles at the center intercept equal arcs on the circumference ; and , conversely , if the intercepted arcs are equal , the angles made by the**radii**are also equal . Let A CB and D CE be equal angles made by**radii**...### 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.